790 ieee transactions on communications, vol. 65, no. 2,...

790 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 65, NO. 2, FEBRUARY 2017

Random Linear Network Coding for WirelessLayered Video Broadcast: General Design

Methods for Adaptive Feedback-FreeTransmission

Mohammad Esmaeilzadeh, Student Member, IEEE, Parastoo Sadeghi, Senior Member, IEEE,and Neda Aboutorab, Member, IEEE

Abstract— This paper studies the problem of broadcastinglayered video streams over heterogeneous single-hop wirelessnetworks using feedback-free random linear network cod-ing (RLNC). We combine RLNC with unequal error protec-tion (UEP) and our main purpose is twofold: to systematicallyinvestigate the benefits of UEP+RLNC layered approach inservicing users with different reception capabilities and to studythe effect of not using feedback, by comparing feedback-freeschemes with idealistic full-feedback schemes. To these ends,we study “expected percentage of decoded frames” as a keycontent-independent performance metric and propose a generalframework for calculation of this metric, which can highlight theeffect of key system, video, and channel parameters. We studythe effect of number of layers and propose a scheme that selectsthe optimum number of layers adaptively to achieve the highestperformance. Assessing the proposed schemes with real H.264 teststreams, the trade-offs among the users’ performances arediscussed and the gain of adaptive selection of number of layersto improve the trade-offs is shown. Furthermore, it is observedthat the performance gap between the proposed feedback-freescheme and the idealistic scheme is very small and the adaptiveselection of number of video layers further closes the gap.

Index Terms— Random linear network coding, layered videostreaming, wireless broadcast.

I. INTRODUCTION

S INCE the introduction of network coding (NC) in [1],this technique has gained much attention and popularity

in different areas of wired and wireless communications.Thanks to its capability in improving bandwidth utilizationand reducing transmission delay and energy, NC has fittedwell into different delay-sensitive applications. One importantexample of such applications that is particularly challengingis NC for video streaming [2].

Manuscript received August 14, 2016; accepted November 7, 2016. Date ofpublication November 17, 2016; date of current version February 14, 2017.This work was supported under the Australian Research Council DiscoveryProjects and Linkage Projects funding schemes (project nos. DP120100160and LP100100588). The associate editor coordinating the review of this paperand approving it for publication was M. Grangetto.

M. Esmaeilzadeh and P. Sadeghi are with the Research School ofEngineering, Australian National University, Canberra 2601, ACT, Australia(e-mail:[email protected];[email protected]).

N. Aboutorab is with the School of Engineering and InformationTechnology, University of New South Wales, Canberra 2612, ACT, Australia(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCOMM.2016.2630062

In video streaming, timely delivery of reliable and qualitycontent is desirable. While the demand for such video serviceis growing exponentially [3], providing the required quality ofservice is often hindered by delay, packet loss and bandwidthlimitations. These challenges are even more restrictive whenvideo is transmitted over dense wireless networks. To dealwith these challenges, a number of useful features has beenadded to wireless technologies and video streaming standards.For instance, point-to-multipoint transmission of video contentis supported in 4G networks through the evolved Multime-dia Broadcast and Multicast Service (eMBMS) [4] frame-work. Another example is the scalable video coding (SVC)of H.264 [5] that provides layered video streams with variouslevels of quality and can be useful when heterogeneity in users’reception/display capabilities exists.

While the added features can mitigate the video streamingchallenges to some extent, combining the layered approachwith forward error correction (FEC) techniques has shownto be even more beneficial [6], as it provides unequal errorprotection (UEP) for different importance layers and thequality of video streaming can be further improved. Someexamples of such approach are studied for Reed-Solomon andFountain codes in [7] and [8], respectively.

In this paper, we focus on random linear NC (RLNC)as a rateless FEC technique and investigate broadcastingof layered video. The selection of RLNC is justified byits superior capability of extension to general networks(by re-encoding at intermediate nodes) that end-to-endFEC techniques (e.g., LT [9] and Raptor [10] codes) do notshare [11]. Furthermore, RLNC can provide better trade-offsamong bandwidth efficiency, complexity and delay, comparedto other FEC techniques [2].

As one of the early works in the context of NC forvideo streaming, we can refer to [12], where video-awareopportunistic NC over wireless networks is proposed. In thisstudy, the importance of video packets based on the deadline,contribution to the video quality and decodability by severalusers is first determined. Then, efficient network codes tomaximize the overall video quality are selected. Assessingthe proposed scheme for different network topologies, signif-icant gain of the video-aware opportunistic NC over schedul-ing algorithms without NC is shown. Another research that

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ESMAEILZADEH et al.: RANDOM LINEAR NETWORK CODING FOR WIRELESS LAYERED VIDEO BROADCAST 791

similarly considers quality and deadline of video packetsis conducted in [13]. In this study, the authors considerlayered video streams and propose to use the finite horizonMarkov decision process (MDP) to select efficient networkcodes. Their scheme shows to outperform non-NC schemes inmultiuser single-hop wireless networks for both broadcast andmultiple unicasts scenarios.

In [12] and [13] feedback-based NC is used. While thistype of NC has many favorable characteristics, the depen-dency of code selection on packet delivery acknowledgments(feedback) makes it unsuitable for some systems/networkssuch as large-scale broadcast networks or large-latency net-works. Hence, RLNC that has lower dependency on feedbackis studied for video streaming [14]–[18]. In these studies,the authors utilize layered video and propose to combineUEP with RLNC (referred to as ‘UEP+RLNC’ in this paper)to achieve an improved performance over non-NC schemes.In particular, [14] proposes an RLNC framework for videostreaming in content delivery networks (CDNs) and peer-to-peer (P2P) networks, where multiple servers/peers areemployed to stream a video to a single user. The authorsin [15] and [17] consider distributed video delivery over lossyoverlay and P2P overlay networks, respectively; [16] studiesvideo streaming using RLNC for single receiver settings andin [18], joint optimization of RLNC and resource-allocationmethods for video streaming over generic cellular systems isinvestigated.

In [14] and [16], the method of coding across layers(i.e., inter-layer coding), as one step forward compared tocoding only within layers (i.e., intra-layer coding) is pro-posed. In this approach, which is referred to as hierarchicalNC in [14], multiple expanding windows (EW) [16] areproposed to generate RLNC packets. Then, using a proba-bilistic approach for selecting coding windows, the decod-ing probabilities of different layers of video are obtainedand the gain of inter-layer UEP+RLNC over intra-layerUEP+RLNC is shown. The authors in [18] consider bothintra- and inter-layer UEP+RLNC for Point-to-Multipointservices over multiple orthogonal broadcast erasure subchan-nels. They formulate packet error probability expression andincorporate it into their resource allocation frameworks [19]to investigate the advantage of layered NC over multiratetransmission. They adapt their framework to 3GPP Long TermEvolution-Advanced (LTE-A) standard and demonstrate theimprovement in the quality of received H.264/SVC video.

In addition to [14], the mentioned hierarchical NC techniqueis used for layered video transmission over P2P networksin [17] and [20] as well. In [17], a pull-based protocol bymeans of distributed resource allocation is proposed, whichrelies on periodic transmission of buffer states between peers.In contrast, the study in [20], which is more similar to ourcentralized feedback-free approach, investigates a push-basedprotocol that calculates the optimized transmission of codedpackets in advance and thus does not need to update the bufferstates or request packets periodically. This is shown to improvebandwidth usage and delay performance.

While the aforementioned studies have confirmed theapplicability of EW UEP+RLNC for streaming of layered

video, a systematic study of this approach for multi-userbroadcast of live H.264/SVC layered video over wireless net-work is still missing in the literature. In particular, a questionof practical importance is how this layered approach canbenefit users with different reception capabilities. Furthermore,previous studies have focused only on either feedback-freeschemes or schemes using periodic feedback, thus a compar-ative study that considers both schemes to quantify the per-formance degradation due to not using feedback is essential.In order to address these issues, the main focus in this paperwill be on EW UEP+RLNC for live streaming of layeredvideo with the aim to:

• design optimal (in the sense we will describe below)feedback-free broadcast schemes over single-hop hetero-geneous erasure channels,

• systematically compare the optimal feedback-freeschemes with idealistic full-feedback schemes.

These are the main theoretical contributions of this paper.We build upon the analysis in [16] and start with the

single-user case and then extend the study to the multi-user case. However, instead of the probabilistic approach forselecting coding windows for transmissions, we consider adeterministic approach, where the number of coded packetsfrom each window is explicitly determined at the sender.In fact, the probabilistic approach in [16] is used to cancel outthe effect of erasure statistics, which is what we actually wantto highlight and study for heterogeneous multi-user networks.Furthermore, with the deterministic approach, we are in factreducing one level of uncertainty in our system design andimplementations, thus our theoretical predictions are expectedto be achieved with more robustness.

To design the optimal schemes, in contrast to studies that usePSNR as the design metric, e.g., [12], [13], [17], [20], we useand maximize a more objective, content-independent perfor-mance metric, which is defined based on the layer decodingprobabilities and can describe the expected percentage ofdecoded frames. This theoretical metric is advantageous overPSNR as its value does not depend on the actual content ofvideo frames, but only on the number of packets of videoframes. Therefore, it can be computed offline as look-up tablesto save computation time during live streaming.

The framework we propose for obtaining this theoreticalperformance metric is general and can be calculated for differ-ent video and system parameters, e.g., packet error rate (PER),number of packets per layer, number of layers and numberof possible transmissions. In addition to studying the effectof different parameters, we propose an adaptive approach forselecting the optimum number of video layers for each groupof picture (GOP, which is the building block of the encodedvideo streams). To this end, when performing fragmentationand aggregation of encoded video data to form packets andlayers, we take into account the expected theoretical perfor-mance metric for different number of layers and choose theone that gives the best expected performance. This is the mainpractical contribution of this study.

To put our results into perspective and compare withfull-feedback scheme as an upper-bound, we study an ideal-istic EW UEP+RLNC scheme, where perfect and immediate


Fig. 1. System model showing different components and their relations. NT∗is specific to feedback-free scheme, the immediate feedback and π(s, t) shown

in dashed line are specific to full-feedback scheme. Moreover, considering different number of layers L and consequently the optimum one, L∗, is specificto opt-layer approaches. These are all discussed in corresponding future sections.

feedback about users’ reception status is assumed to be avail-able at the sender. We utilize the finite horizon MDP [21]to obtain the optimal performance of this idealistic schemeand then compare it with our proposed feedback-free scheme.We note that MDP has been utilized for streaming applicationsin different setups, e.g., for rate-distortion optimized stream-ing of packetized media in [22], for dynamically optimizedmulti-user wireless video transmission in [23], for adaptivescheduling of stored scalable video in [24] and for adaptivecoding and scheduling of layered video from multiple serversin [25], which are all totally different to our application inthis study; Here we adapt MDP to the problem of layeredstreaming using EW UEP+RLNC.

To assess the performance of the designed optimal schemeswe use real H.264/SVC encoded video test streams andconsider various systems parameters. We show the proposedfeedback-free scheme performs close to the idealistic scheme.Furthermore, the gain of using optimum number of layers overusing fixed number of layers is clearly shown. Finally, to betterstudy the effect of heterogeneity of users’ erasure channels onthe defined theoretical performance metric, we incorporate thefairness of users’ performances into the broadcast design anddiscuss the performance trade-offs.

The remainder of the paper is organized as follows. The sys-tem model, transmission schemes and the performance metricsare presented in Section II. In Section III, we formulatethe decoding probabilities of different layers and define thetheoretical performance metric for the single-user case. Then,we discuss the extension to the multi-user case in Section IV.Section V briefly describes the H.264/SVC video test streamsand the PSNR calculation. The numerical results are providedin Section VI, and finally Section VII concludes the paper.

II. SYSTEM MODEL

The system model consists of a sender and a set of Nu

wireless users. The channels between the users and the senderare assumed to be independent and heterogeneous, i.e., theyare not necessarily identical and have packet error rates (PERs)of Pei , 1 ≤ i ≤ Nu . The sender is supposed to broadcast alive layered video stream to the users. We consider that thelayered video data is chunked, where each chunk correspondsto a fixed number of frames that we refer to as a groupof picture (GOP), to be compliant with video streamingstandards.

Each GOP is composed of M packets x1, . . . , xM , whichare from L layers. Layer 1 is considered to be the mostimportant layer and layer L is the least important one. Packetsof layer � are useful only if all packets of lower layers arereceived (decoded) correctly. We consider layer � to have k�

packets, thus∑L

�=1 k� = M . We use K = [k1, k2, . . . , kL ] todenote the number of packets from different layers in a GOP.For real video test streams, depending on the video content,M and K can take different values for different GOPs.

We apply our NC approach on the packets of each GOP assoon as they are all ready, which means neither merging ofGOPs nor buffering of packets is considered. This is importantin live streaming to minimize the delivery delay. For anyGOP of interest, considering that the number of frames perGOP is F , video frame rate is f frames per second (fps),the transmission rate is r bits per second (bps) and theselected packet length is n bits, the possible number of packettransmissions for one GOP is fixed and limited. We denote thisnumber by Nt and it can be inferred that Nt = Fr

n f . This isin fact the deadline for delivering the packets in each GOP tothe receivers and thus our considered model is suitable for livestreaming as long as the number of transmissions is confinedto Nt .

A schematic model of the considered system is depictedin Fig. 1. Different system blocks are discussed in corre-sponding sections: RLNC layered encoding and transmittingin Sections II-A and II-B, Performance estimation and systemdesign in Sections III and IV, and H.264/SVC encoding andPacketization in Section V.

A. Random Linear Network Coding (RLNC)

Similar to [16], we utilize RLNC [26] in this study and usecoding over expanding windows. In this approach, L codingwindows are considered, where �-th window, denoted by W�,contains all packets from layers 1 to � as shown in Fig. 2.Then, based on the transmission policy, network coded pack-ets from different windows are generated and transmitted.This approach is often considered in contrast to coding overnon-overlapping windows (NOW) [16], where coding windowW� contains only packets of layer �. In fact, coding usingNOW considers only intra-layer NC, but coding using EWallows for inter-layer NC in addition to intra-layer NC. Con-sequently, in the EW approach, packets of more importantlayers are protected better and are more likely to get decoded


TABLE I

COMPARING DECODING OUTCOME OF THE EW AND NOW APPROACHES FOR TWO ERASURE PATTERNS EXAMPLES

Fig. 2. An L-layer GOP with k� packets in the �-th layer. Examples of theexpanding windows are shown.

compared to the NOW approach, as shown in the upcomingExample 1.

The theory behind RLNC encoding, decoding, code effi-ciency and decoding complexity has been studied compre-hensively in the literature during the past decade [26], [27],with the effect of field size q also discussed indetail (e.g., [11], [28]). Hence, we do not elaborate on theseissues here. We assume the encodings are over large enoughfield sizes, which leads us to the following remarks:

Remark 1: The coded packets generated from packets ofa coding window are all linearly independent (with highprobability, which we approximate to be one).

Remark 2: Considering the EW approach, in order todecode all the packets of a coding window W�1 ,

∑�1�=1 k�

linearly independent coded packets from W�1 windoware required. With the assumption of large enough fieldsizes, coded packets from smaller windows, i.e., W�2 with1 ≤ �2 < �1 can also be used in decoding, but with a limitationthat for every �2, the total number of coded packets fromwindows W1 to W�2 does not exceed

∑�2�=1 k�.

These remarks are used to obtain the decoding probabilitiesfor our approach in the next section. We note that althoughwe assume large field sizes and disregard that the effect offield size q in decoding probabilities, this can be later incor-porated in our study, as has been discussed in [16] and [29].Furthermore, decoding complexity, which is the flip side ofRLNC specially when q is large, can be alleviated by usingsystematic [30], [31] and sparse [32], [33] implementationsof RLNC.

To make the remarks more clear, let us consider the follow-ing simple example that also provides comparison betweenEW and NOW approaches.

Example 1: In this example, we consider L = 2 layers andassume that k1 = k2 = 2, i.e., packets x1 and x2 are fromthe first layer and packets x3 and x4 are from the secondlayer. We use y�

i to denote the i -th coded packet from the�-th window, which is obtained as y�

i = ∑x j ∈W�

ai, j x j .Here, W1 contains packets x1 and x2 for both the EW andNOW approaches, W2 contains all the four packets in the EWapproach, but only packets x3 and x4 in the NOW approach,

and ai, j ’s are the randomly chosen coefficients from Fq .Considering that Nt = 6 transmissions are possible, Table Iprovides two different erasure patterns examples and comparesthe decoding outcomes for the EW and NOW approaches whenthree coded packets from each of the windows are transmitted.

Considering the first erasure pattern, it can be seen thatEW can decode packets of both layers and thus outperformsthe NOW approach that only decodes packets of the secondlayer, which are useless without packets of the first layer.Moreover, considering the two different erasure patterns for theEW approach, although 4 coded packets are received in totalin both cases, only in the first case both layers are decodable,which is directly concluded from Remarks 1 and 2.

B. Transmission Schemes

In this paper, we consider two transmission schemesboth using the EW approach, a feedback-free RLNC-basedtransmission scheme, and also an idealistic full-feedbackRLNC-based transmission scheme. The purpose is to inves-tigate how close the proposed feedback-free scheme canperform compared to the idealistic upper-bound. Here, the ide-alistic notion of feedback is for the RLNC methods and notfor the whole system. In other words, as shown in Fig. 1,even for the feedback-free scheme, there exist backward linksfrom users to the sender to communicate control signals andstatistical information (e.g., to estimate Pei ) infrequently aslong as the total bandwidth requirements of backward linksare satisfied.

As mentioned previously, based on the system parameters,we assume the sender can transmit at most Nt NC packetsfor each GOP. Here we explain how these transmissions arecarried out for each of these schemes and will formulate theirperformance in the next section.

1) Feedback-Free Scheme: In this scheme, for each GOP,the sender decides in advance on the number of codedpackets from each coding window that should be transmit-ted, and then sends them one after another, without waitingfor any feedback. Assuming that nt

� packets are generated(and thus transmitted) from the packets in the �-th window,then

∑L�=1 nt

� = Nt and we call NT = [nt1, nt

2, . . . , ntL ]

a feedback-free transmission policy. The decision on theoptimum policy is made based on an aggregate function ofusers’ performance by taking into account Nt and channelscharacteristics. This will be discussed in Section IV.

2) Full-Feedback Scheme: In this idealistic scheme, it isassumed that the sender knows exactly how many packetsof different windows each user has received so far. Hence,based on this information, channels characteristics, and theremaining number of transmissions from total Nt , the senderdecides on the next transmission to optimize an aggregatefunction of users’ performance. Since we have considered L


windows for generation of coded packets, the sender should infact decide on the coding window from which the next packetfor transmission is generated.

C. Performance Metrics

In this paper, we will consider two types of performancemetrics. The main metric that we use for our systems designs,is the weighted sum of the layer decoding probabilities, whichis theoretical and content-independent, i.e., does not dependon the actual video content, but on the number of videopackets. Based on the selection of the weights, this metriccan reveal, for example, the expected percentage of decodedframes or the expected throughput. The formulation of thismetric is presented in Sections III and IV. In the resultssection, in addition to obtaining the average values for thetheoretical performance metric, we also calculate the averagePSNR as it is a widely used metric for video quality. PSNRcalculations are described in Section V.

III. FORMULATION OF THEORETICAL PERFORMANCE

METRICS – SINGLE-USER CASE

In this section, we present the formulation of the theoreticalperformance metric of the feedback-free and full-feedbackschemes for the single-user case, and then will discuss theirextension to the multi-user case in the next section. Thesetwo sections in fact build the framework for Performanceestimation and system design block illustrated in Fig. 1.

A. Feedback-Free Scheme

Under the assumptions made in Section II, we start withformulating the probability that a user with PER of Pe candecode the packets of layer � (and of course all the packets oflower layers). We denote this probability by P�(K, NT). Then,we define the expected theoretical performance metric as theweighted sum of these probabilities for all 1 ≤ � ≤ L.

To obtain these probabilities, we assume that out of thent

� coded packets of the �-th layer, nr� packets are received,

where 0 ≤ nr� ≤ nt

�. We denote by NR = [nr1, nr

2, . . . , nrL ]

the number of received packets from different layers. Then,considering all possible NR, P�(K, NT) can be written as

P�(K, NT) =∑

all possible NR

P(NR|NT)I (Lmax (K, NR) = �)

(1)

where

P(NR|NT) =L∏

�=1

(nt

�

nr�

)

(1 − Pe)nr

� Pnt

�−nr�

e (2)

I (·) is an indicator function with output 1 if its argument,which is a logical expression, is true.

The function Lmax(K, NR) calculates the highest decodablelayer based on Remarks 1 and 2. The value for this functioncan be calculated as follows

Lmax(K, NR) = max{D(1), D(2), . . . , D(L)} (3)

where D(�) is equal to � when packets of window � are alldecodable and zero otherwise. Hence, D(1) = I (nr

1 ≥ k1)

TABLE II

STEPS FOR CALCULATION OF Lmax (K, NR) USING K = [5, 1, 2, 3] AND

NR = [4, 3, 1, 3]. HENCE, THE FIRST TWO LAYERS CAN BE DECODED

and D(�) for 2 ≤ � ≤ L are calculated using the followingrecursive formulas:

b(�) = max{D(1), . . . , D(� − 1)} (4)

D(�) = � × I

⎛

⎝�∑

i=b(�)+1

nri ≥

�∑

i=b(�)+1

ki

⎞

⎠ (5)

In fact in every iteration, b(�) holds the index of the largestdecodable window from previous iterations, and then thedecoding condition in (5) is tested for the remaining unde-coded packets. Some sample outputs of the Lmax(K, NR)function are presented in the following example and thecalculation steps for one of the samples are given in Table II.

Example 2: Considering K = [5, 1, 2, 3], the outputs ofLmax(K, NR) function for NR = [4, 1, 2, 3], NR = [5, 0, 2, 3],NR = [4, 3, 1, 3], NR = [0, 4, 4, 2] and NR = [3, 0, 0, 8] are0, 1, 2, 3 and 4, respectively.

Having calculated the layer decoding probabilities, the the-oretical performance metric can be defined as follows

η =L∑

�=1

c� P�(K, NT) (6)

where c� reflects the cumulative importance of layers 1 to�. For instance, considering the temporal scalability in SVCof H.264, for a 2-layer case, if the number of frames perlayer are equal, with c1 = 0.5 and c2 = 1, η will give theexpected percentage of decoded frames. The explanations inSection V will better clarify this. As another example, if wecan consider c� to be the ratio of the number of packetsobtained by decoding layer � to the total number of packets as

c� =∑�

j=1 k j∑L

j=1 k j, (7)

then η will give the expected throughput. We emphasize thatthe metric defined in (6) is a general metric and caters for anyother weighting as required by the application.

With the theoretical formulation for η obtained in (6),the optimal feedback-free policy for the single-user case canbe acquired by

NT∗ = arg maxnt

1,...,ntL

{η}, subject toL∑

�=1

nt� = Nt (8)

which is solved in Section VI by exhaustively searchingthrough all possible combinations of [nt

1, . . . , ntL ] that are at

most (Nt )L cases. Assuming the time complexity of calcu-

lating η (using (1)-(6)) for different NT is upper-bounded by


�η(Nt , L), the optimization in (8) has overall time complexitysmaller than O(�η(Nt , L).(Nt )

L).

B. Full-Feedback Scheme

In this section, the objective is to obtain the formulationof a similar theoretic performance metric as in (6) for thefull-feedback scheme. To this end, we utilize the finite horizonMarkov decision process (MDP) [21].

In the full-feedback scheme, before every transmission thesender should decide on what to transmit next. The decisionis made to optimize the performance metric by consideringthe immediate information about the reception status of theuser, the channel status, as well as the remaining number oftransmissions. Here, since the number of transmissions Nt

is limited, this can be best modeled by the finite horizonMDP, with Nt horizons (stages). A summary of finite horizonMDP is presented in Appendix A. Here, we will explain howthe different components of MDP should be assigned in ourconsidered scenario.

1) States: For the states, we consider an L-tuple s =(d1, d2, . . . , dL), where each 0 ≤ d� ≤ k� element showsthe remaining required independent packets to decode layer �.Thus, it is obvious that at the start of the transmission, the stateis s0 = (k1, k2, . . . , kL) and the state space Ssingle has a sizeof |Ssingle| = ∏L

�=1(k� + 1).2) Actions: For the actions, we consider L different actions

A = {a1, . . . , aL}, where in action a�, a coded packet gen-erated from packets of the coding window W� is transmitted.Under action a�, if the coded packet is received correctly (withprobability 1 − Pe), then a change in state occurs if at leastone of the d1 to d� is nonzero. Otherwise, if all of the d1 tod� are zero, state will not change. In fact, the latter shows acase where all the packets of the first � layers are successfullydecoded, so a coded packet from the �-th layer does not giveany extra information. It is apparent that in the case of notreceiving the coded packet (with probability Pe), the stateremains unchanged. An example of this is shown in Fig. 3,assuming the coded packet is received, L = 3 and startingstate s0 = (1, 1, 1).

3) State Transition Probabilities: Now, considering the statetransitions caused by actions, we first define the state transitionfunction with the assumption of successful reception of codedpackets and then obtain the state transition probabilities.We assume the current state is s = (d1, d2, . . . , dL) and wantto obtain next state sn = (dn

1 , dn2 , . . . , dn

L) following an actiona�. Function F(s, a�) calculate sn as follows

sn = F(s, a�)

=

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(d1, . . . , d� − 1, . . . , dL); d� �= 0

(d1, . . . , di∗ − 1, . . . , dL); d� = 0 &

∃ i ∈ {1, . . . , � − 1} :di �= 0

i∗ = max{i}(d1, . . . , dL); ∀ i ∈ {1, . . . , �} : di = 0

(9)

To clarify how this function works, we use the exam-ple in Fig. 3 and consider state (1, 1, 0). Following

Fig. 3. An example of states, actions and terminal rewards. Terminal rewardsfor other states are zero.

actions a1 and a2, transitions to states (0, 1, 0) and (1, 0, 0),respectively, are straightforward as both d1 and d2 are nonzero.For action a3, since d3 is zero, from d2 and d1, d2 is reducedby one for the next state, as it has the largest index among thenonzero d�. This is to assure that enough independent packetsare received before decoding of layers and is better understoodin conjunction with the definition of terminal reward functionsin Section III-B.4.

Using F(s, a�), the state transition probabilitiesPsingle(s|s, a�) for any s, s ∈ Ssingle and a� ∈ A can beobtained by

Psingle(s|s, a�) = (1 − Pe)I (s = F(s, a�)) + Pe I (s = s) (10)

4) Reward and Terminal Reward Functions: We considerthe reward function R(s, a) to be zero for all s ∈ Ssingle and a ∈A and use only the terminal reward Gsingle(s) to capture theeffect of layer decoding on the theoretical performance metric.This approach is valid because the state in which the user iswhen the transmission has finished is important in calculationof the performance metric in this scheme, but not how or whenit has reached that state. Hence, using the same idea shownin Fig. 3 for terminal rewards, the terminal reward can beobtained, in general, as follows

Gsingle(s) =

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

R�∗; ∃ � ∈ {1, . . . , L} :�∑

i=1

d� = 0

�∗ = max{�}0; otherwise

(11)

Here, reward of R1 means that only packets of the first layerare decoded and reward of R� means that packets of layer �and all the lowers layer are decoded.

Back to the example in Fig. 3, it can be observed that ifwe start from state (1, 1, 1), in the case of one successfulaction a1 and one successful action a3 (regardless of the order),we end up in state (0, 1, 0) and only first layer is decodable.Hence, reward of R1 is given. In another case, with only twosuccessful a3 actions, the final state will be (1, 0, 0) and eventhe first layer cannot be decoded. Thus reward is zero.


Having discussed all the elements of finite horizon MDP,the optimal theoretical performance metric is the value func-tion1 at stage 1 (i.e., Nt transmissions to go) for state s0 =(k1, k2, . . . , kL) defined as

η = V Ntπ (s0) (12)

Note that, in contrast to the formulation for thefeedback-free scheme (8) that required a single optimizationto obtain the optimal policy, the proposed solution for thefull-feedback scheme, which is based on finite horizon MDP,requires an optimization at every stage, hence the η givenin (12) is optimal and the optimal policy is in fact given bythe obtained optimal actions for different states and stages,i.e., π(s, t) for s ∈ Ssingle and 1 ≤ t ≤ T . As dis-cussed in Appendix A, this method has time complexity ofO(Nt L|Ssingle|2). In order for the metric in (12) to measurevalues with similar meaning as in (6), it is required thatR� = c�.

IV. FORMULATION OF THEORETICAL PERFORMANCE

METRICS – MULTI-USER CASE

In this section, the objective is to discuss how the for-mulations in the previous section can be used and extendedto the multi-user case in order to design RLNC-based videostreaming. As stated in the system model, Nu wireless userswith independent and heterogeneous erasure channels areconsidered and the purpose is to optimize an aggregation oftheir performance metrics.

A. Feedback-Free Scheme

For this scheme, the performance metric of user i withPei , 1 ≤ i ≤ Nu , which is denoted by ηi , can be obtainedindependently by using (6) for any K and NT. Then theaggregate performance metric is defined as

ηtot = H (η1, . . . , ηNu ) (13)

where H (·) is the considered aggregate function. Hence,the optimal policy will be obtained as

NT∗ = arg maxnt

1,...,ntL

{ηtot}, subject toL∑

�=1

nt� = Nt (14)

We note that various functions can be considered for H (·)(such as mean, geometric mean, functions that consider theperformances of a subset of users or even functions that com-bine different performance metrics to study their trade-offs),which allow the sender to decide on how to allocate thebandwidth to the transmission of coded packets from differentlayers. The decision about this is made based on the networkconfiguration and the requirements of applications.

B. Full-Feedback Scheme

The extension of the single-user’s formulation to multi-usercase for the full-feedback scheme is more complicated com-pared to the feedback-free scheme discussed in the previoussubsection. This is due to the fact that in the full-feedback

1V tπ (s), this is defined in Appendix A.

scheme, decisions about the coded packets to be transmittedare made based on the reception status of all or a subset ofusers before every transmission. Hence, the performance ofeach user, in addition to its own reception, is dependent uponthe reception of other users. This makes the finite horizonMDP problem more complicated.

To obtain the input components of the finite horizon MDP,we consider the same function H (·) to calculate the aggregateperformance metric. Considering that the performances of asubset of nu users (out of Nu ) are taken into account inthe sender’s decisions (1 ≤ nu ≤ Nu ), it can be easilyinferred that the multi-user state space Smulti has a size of|Smulti| = |Ssingle|nu . Then, a state s ∈ Smulti is defined withan nu-tuple (s1, . . . , snu ), where each sj ∈ Ssingle is itself anL-tuple, as defined in Section III-B, showing the state foruser j , 1 ≤ j ≤ nu .

Since the actions are similar to the single-user case, the nextcomponent to be computed is the transition probability func-tion. For any s, s ∈ Smulti, the transition probability functionPmulti(s|s, a) can be calculated as

Pmulti(s|s, a) =nu∏

j=1

Psingle(sj|sj, a) (15)

where sj, sj ∈ Ssingle. In fact, the state transitions causedby action a are independent for different users, thus themultiplication of the single-user transition probability func-tions Psingle(sj|sj, a) gives the multi-user transition probabilityfunction.

For the reward functions, we again assume that R(s, a)has zero value for all the actions and states. Then, in orderto properly model the reward in every state s ∈ Smulti,the terminal reward Gmulti(s) should be defined as follows

Gmulti(s) = H (Gsingle(s1), . . . , Gsingle(snu )) (16)

Having defined all the components for the multi-user finitehorizon MDP, the optimal theoretical performance metric isthe value function at stage 1 for state s0

multi = (s01, . . . , s0

nu),

where s0j = (k1, k2, . . . , kL) for every user 1 ≤ j ≤ nu .

Hence, the aggregate performance metric is given by the valuefunction at stage 1 for state s0

multi, as follows

ηtot = V Ntπ (s0

multi) (17)

which requires calculation of V tπ(s) and π(s, t) for every s ∈

Smulti and 1 ≤ t ≤ Nt .

C. On the Computational Complexities of Multi-UserSchemes

In this subsection, we briefly discuss the computationalcomplexities of the feedback-free and full-feedback schemeswhen nu users (out of Nu ) are considered for multi-user systemdesign.

Regarding the feedback-free scheme, since ηi can becalculated independently for different users, the complex-ity increases linearly with nu . Hence, solving the optimiza-tion in (14) exhaustively has time complexity smaller thanO(nu�η(Nt , L) · (Nt )

L).


Fig. 4. A closed GOP with 8 frames, constituted by I, P and B frames.

For the full-feedback scheme, as the size of the statespace increases exponentially, the computational complexityof obtaining the optimum policies (actions) also grows expo-nentially, i.e., O(Nt L|Ssingle|2nu ).

While the exponential complexity is not desirable,we emphasize that the proposed full-feedback scheme is anidealistic scheme used as a benchmark. Furthermore, althoughwe will select nu to be equal to the total number of users (Nu )in our simulations, it is possible to judiciously design thesystem based on a subset of users, as in [11], to keep thecomplexity reasonable. Moreover, many of the optimizationsteps that require demanding computations do not need to becalculated online for every GOP. Instead, they can be tabu-lated (as look-up tables, LUTs) for expected more commonsystem parameters offline, or LUTs can even be graduallyfilled as the system is trained.

V. SVC VIDEO STREAMS AND PSNR CALCULATIONS

This section provides details about the H.264/SVC videotest streams used in this paper and also briefly explains thePSNR calculations.

We consider three standard video streams: Foreman, Crewand Soccer [34]. These streams are all in common interme-diate format (CIF, i.e., 352 × 288) and all have 300 frameswith 30 fps. To encode the video streams using the JSVMreference software of H.264/SVC codec [5], [35], we considerclosed GOP structure, which means the encoding/decodingof the frames inside a GOP is independent of frames out-side the GOP, so that GOPs can be analyzed independently.Furthermore, we select the GOP size equal to F = 8 framesso that it is easily devisable by two when considering 2,3 and 4 layers. With the mentioned settings and by benefitingonly from the temporal scalability of H.264,2 38 GOPs areobtained for each stream with PPBPBBBI structure. This isshown in Fig. 4 by using gray shades, where the darker theshade, the more important the frame(s).

Having obtained the encoded frames shown in Fig. 4,the information bits should be assigned to the layers andpackets. To this end, we consider n = 1500 bytes as the packetlength, which is the maximum transmission unit (MTU) overEthernet and is also used in some wireless technologies and

2The proposed framework for calculating the expected theoretical per-formance metric is general and can be easily applied to other scalabilitytypes (e.g., spatial and quality). Furthermore, as the framework treats eachGOP separately, GOPs with variable number of frames and/or other structurescan also be considered.

standards [36]–[38]. Assuming 100 bytes are dedicated to allthe header information, ne f f = 1400 bytes are used for videodata. Then, we do aggregation and fragmentation of infor-mation bits of different frames to form packets. Consideringthat the encoded frame i, 1 ≤ i ≤ 8, is composed of mi

bytes, the easiest way to assign video information to layers

and packets would be the 1-layer case with k1 = ∑8

i=1 minef f

packets. For the 2-layer case, we choose k1 = m2+m4+m6+m8

ne f f

and k2 = m1+m3+m5+m7nef f

. For the 3-layer case, packets per

layer can be considered as k1 = m4+m8ne f f

, k2 = m2+m6nef f

and k3 = m1+m3+m5+m7

ne f f and finally for the 4-layer case,

we consider k1 = m8ne f f

, k2 = m4nef f

, k3 = m2+m6ne f f

and

k4 = m1+m3+m5+m7ne f f

.Remark 3: It should be noted that the number of packets

for each expanding window shown in Fig. 2, is the sum of thenumber of packets per layer within that window. However,due to using the ceiling function ·, for any GOP of interestthe sum of calculated k�1 for an L1-layer case (�1 ≤ L1)can be smaller than the sum of calculated k�2 for an L2-layercase (�2 ≤ L2) when L1 < L2. For example, consideringthe Foreman video stream, the number of packets per layeraveraged over 38 GOPs is obtained as K = [13.32] for1-layer case, where for 2-layer and 3-layer cases they areobtained as K = [11.92, 2.11] and K = [10.24, 1.95, 2.11],respectively. In other words, the total number of packets Mis affected by the number of layers L. This will have aneffect on the performance metrics too. Therefore, in additionto the approaches that use fixed number of layers, which werefer to as ‘L-layer’ approaches, we also study an approachthat adaptively selects the optimum number of layers basedon Nt and K for each GOP such that the highest theoreticalperformance is achieved for that GOP. This is referred to as‘opt-layer’ approach and its performance is later discussedin Section VI-B.

Remark 4: The defined 1-layer case only offers nominaltemporal resolution of 30 fps for each GOP, i.e., either all8 frames of a GOP are decoded or none are decoded, whereasthe other cases provide more temporal resolutions, e.g., for the4-layer case, nominal temporal resolution of 3.75, 7.5, 15 and30 fps are possible for each GOP, which correspond to 1, 2,4 or 8 decoded frames out of 8. Hence, back to performancemetric calculation in Section III-A, to obtain the expectedpercentage of decoded frames, c� should be selected as c1 = 1for the 1-layer case and c1 = 1/8, c2 = 1/4, c3 = 1/2 andc4 = 1 for the 4-layer case, which can be written in the generalform of c� = 2�−L .

To utilize PSNR as a performance metric, we use theluminance (Y) component of video sequences and obtainσi1,i2 , which is the Y-PSNR if the uncompressed i1-th frameis replaced by the compressed (i.e., encoded) i2-th frames(for 1 ≤ i1, i2 ≤ 300). Considering Yi1 and Yi2 matrices asY components of frames i1 and i2, respectively, σi1,i2 is cal-culated as 10 log10(2552/M SE(Yi1 , Yi2 )); function M SE(·)measures the mean square error between Yi1 and Yi2 .

Having obtained the PSNR values σi1,i2 , we then calculatethe average PSNR of each GOP, if only � layers (0 ≤ � ≤ L)


Fig. 5. An example of using the nearest decoded frames to conceal the lossof undecoded frames.

are decodable. To this end, the frames of the undecodable lay-ers of the current GOP are replaced by the nearest frames (intime) of decodable layers of current or previous GOPs. Thisis to conceal the errors. Therefore, the average PSNR of theg-th GOP is obtained as

σg =(∑

i∈D

σi,i +∑

i /∈D

σi, j (i)

)/8 (18)

where the set D holds the indices of the frames of thedecocable layers of the g-th GOP and j (i) represents the indexof the nearest decodable frame to the i -th frame.

To make the PSNR calculation more clear, let us considerthe following example.

Example 3: We consider a 4-layer case, as shown in Fig. 4,and assume that for the g-th GOP, the 3rd layer (and conse-quently the 4th one) is lost. If the I frame of the (g − 1)-thGOP is decoded, the error concealment can be considered asshown in Fig. 5 and the average PSNR is acquired as

σg = (σk,k−1 + σk+1,k+3 + σk+2,k+3 + σk+3,k+3

+ σk+4,k+3 + σk+5,k+7 + σk+6,k+7 + σk+7,k+7)/8 (19)

which means the (k − 1)-th frame is displayed to conceal theloss of the k-th frame. In another example, if the I frame of the(g−1)-th GOP is not decoded, then (k+3)-th frame is the near-est frame to be displayed to conceal the loss of the k-th frameand the first term in (19) needs to be replaced with σk,k+3.

We note that in practice the calculation of σi1,i2 can bedone at the sender side when video is encoded. Then toobtain the PSNR performance, σg can be calculated at eitherthe sender or the user side. For the former, the receptionof number of layers for each GOP can be sent back to thesender infrequently via the available backward link for controlsignals shown in Fig. 1. For the latter, the sender can embedthe information into packet header, e.g., RTP3 [39] extendedheader or part of the network coding header, as explainedin [12] so that the user can calculate σg .

VI. NUMERICAL RESULTS

In this section, we present the numerical results in threemain parts. First, we discuss a simple case for a layered dataand study the effect of the number of layers on the theoreticalperformance metrics. Second, we consider real video streamsand discuss the theoretical performance metric and the PSNR

3Real-time Transport Protocol, a protocol for delivering audio and video

Fig. 6. Optimum expected performance metric versus Nt for M = 10 packetsusing the feedback-free scheme. Different number of layers and consequentlydifferent number of packets per layer are considered as follows: 1-layer withK = [10], 2-layer with K = [4, 6], 3-layer with K = [4, 2, 4] and 4-layerwith K = [4, 2, 2, 2].

performance for the single-user case and finally extend thediscussion to the multi-user case. In each of these parts,the feedback-free scheme is the main focus and we compareits performance with the full-feedback scheme as well as anuncoded scheme, when appropriate. The details of the uncodedscheme and formulations of the theoretical performance metricare provided in Appendix B.

Results in the first part are the evaluation outcomes ofthe analytical expressions in Section III-A and Appendix B.In the second and the third parts, the analytical expressionsin Sections III, IV and Appendix B are used for the sys-tem design and then simulation results are obtained andshown. All the implementations and simulations are donein MATLAB.4 An MDP toolbox [40] is employed for the finitehorizon MDP modeling used in the full-feedback scheme.The optimizations in (8) and (14) are solved by exhaustivelysearching through all possible cases.

A. Theoretical Performance Metric – a Simple Example

We consider a layered data with M = 10 packets. We con-sider up to 4 layers and without loss of generality, ignore theeffect of number of layers on M , mentioned in Remark 3.Hence, we assume 4 different cases with different numberof layers, K = [10], K = [4, 6], K = [4, 2, 4] andK = [4, 2, 2, 2] and calculate the optimum performancemetric for the feedback-free scheme by using (7) and (8).The obtained results for two choices of PER, Pe = 0.1and Pe = 0.3, are depicted in Fig. 6. Each point in thisplot corresponds to an optimal NT∗

, obtained based on Nt ,Pe and L.

Considering the results shown, it can be observed that usingmore layers clearly provides a better performance. However,this improved performance is only for an intermediate range ofNt values, where the number of transmissions is large enough

4We have exploited mex-files to expedite the simulations and MATLABsparse matrix functionalities to reduce the required memory.


Fig. 7. Throughput performance of the feedback-free RLNC and uncodedschemes for Nt = 13. The number of points in some curves is naturally lim-ited; for example when L=1, there is only one point on the curve. Each pointrepresents one Pareto optimal policy for the 2-user case. Parameters M and Kare similar to those used in Fig. 6.

to deliver a subset of packets, but not enough to deliver allthe M packets. It can be seen, and also easily inferred, thatthis range of Nt is dependent upon the PER values, as higherPER values require more transmissions to provide a specificperformance, thus the mentioned range of improvement shiftsto the higher values of Nt as PER increases. We note that ifNt is selected very large compared to M , not only no gainis expected from the layered approach, but the bandwidthmay also be wasted. Hence, we focus on the mentionedintermediate range of Nt to better study the gain and to avoidwaste of bandwidth.

Note that for a chosen Nt , since the optimum policies NT∗

for two users with different PERs are dissimilar, the shownperformances cannot be obtained simultaneously for the multi-user cases. In other words, the optimum policy for a user withPe = 0.1 will result in a worse performance than the oneshown in Fig. 6 for a user with Pe = 0.3. Hence, for themulti-user case, there is a trade-off among the performancesof different users and an absolute optimum NT∗

may not befound. Therefore, Pareto optimal [41] NT∗

for multi-user caseshould be considered. This is shown in Fig. 7 for a 2-user caseusing Nt = 13.

The results in Fig. 7 show that as the number of layers isincreased, more Pareto optimal policies are possible, whichmeans there are more opportunities to optimize and designthe multi-user broadcasting system. This, in fact, implies thatusing more layers results in a better trade-off between theperformances of users. However, similar to the results in Fig. 6,the gain of using more layers is not for every choice of Nt .For instance, for Nt = 20 that is large enough to deliver allthe M = 10 packets, using 4 layers theoretically does notprovide any advantage over a single layer case. Moreover,we should remember that this gain is obtained by ignoringthe effect of number of layers on total number of packets,discussed in Remark 3. In the next subsections, we willconsider this remark and observe its effect on the results.Fig. 4 also compares the feedback-free RLNC scheme with

the feedback-free uncoded scheme. It can be observed thatthe former significantly outperforms the latter.

B. Results for Real Video Streams – Single-User Case

In this subsection, we consider real video test streams andin contrast to the previous subsection, we take into accountthe effect of number of layers L on the total number ofpackets M , discussed in Remark 3. The purpose is to com-pare the performance of the proposed feedback-free and theidealistic full-feedback schemes. Furthermore, we investigatehow adaptive selection of number of layers can improve theperformances of these two schemes and reduce the perfor-mance gap between them, compared to schemes with fixednumber of layers. To this end, for each GOP with knownnumber of packets per layer (K), we first design the optimumtransmission policy, i.e., obtain the NT∗

for the feedback-freescheme and π(s, t) for the full-feedback scheme, based on thevalues of Nt , L, Pe and the calculated theoretical performancemetric. Then, we model the erasure channels and assess howthe designed policies perform under simulations.

To model the erasure channel, we consider time is slottedand each slot is only enough for transmission of one packet of1500 bytes. We assume that the channel is either in ON state,with probability 1 − Pe, or in OFF state, with probability Pe.Hence, we generate random erasure patterns of 38 × Nt long5

containing 0 and 1 elements, where 0 and 1 correspond to theOFF and ON states, respectively.

Given an erasure pattern and the optimum transmissionpolicies, it is straightforward to obtain the highest decodablelayer of both the feedback-free and full-feedback schemes forany GOP, by using (3) and (9), respectively. Then, we cal-culate the performance metrics with regard to the importanceof decoded layers mentioned in Section V. We repeat thisfor 100 different erasure patterns and calculate the averageperformance metrics.

The results in Fig. 8 illustrate the average performancemetrics for both schemes for the Foreman test stream usingPe = 0.1. In addition, Table III highlights the maximum andmean improvement (in the average performance metrics) ofthe full-feedback scheme over the feedback-free scheme for allthe three test streams, where the maximum and mean valuesare calculated across 10 ≤ Nt ≤ 30. Note that the 1-layercase performs similarly in both schemes, as there is only onetype of coded packet for transmission (i.e., only one actionin the finite horizon MDP), so feedback cannot provide anyextra gain. Therefore, the graphs for the 1-layer case can beused as a reference to compare graphs of feedback-free andfull-feedback schemes and it is not presented in Table III asthe improvement is always zero. Here, the main observationscan be summarized as follows

• for the feedback-free scheme, it can be observed thatincreasing the number of layers L does not alwaysimprove the performance. However, this is not surprisingas, according to Remark 3, by increasing L, whichenables decoding of a subset of a GOP’s frames to

5Note that each of the test streams is composed of 38 GOPs, as mentionedin Section V.


Fig. 8. Average percentage of decoded frames and average PSNR for single-user case using Foreman test stream. Feedback-free and full-feedback schemeswith different number of layers are compared. Values are averaged over the 38 GOPs and the 100 repetitions.

TABLE III

MAXIMUM IMPROVEMENT (IN THE AVERAGE PERFORMANCE METRICS) OF FULL-FEEDBACK SCHEME OVER FEEDBACK-FREE SCHEME FOR VARIOUS

TEST STREAMS AND TEST SETUPS. MEANS ARE ALSO PROVIDED IN PARENTHESES

improve the performance, the total number of packetsM may also increase, which can inversely affect theperformance.

• comparing the two schemes, Fig. 8 reveals thatthe feedback-free scheme can perform close to thefull-feedback scheme for the considered Foreman stream.This is confirmed by the detailed results in Table III,which show the full-feedback scheme improves the PSNRby 1 ∼ 2 dB and 2 ∼ 3 dB for users with PERof 0.1 and 0.3, respectively.

• considering the opt-layer approach, it is evident in Fig. 8that it outperforms all other approaches with fixed num-ber of layers in both feedback-free and full-feedbackschemes. Moreover, as Table III suggests, selecting thenumber of layers for each GOP adaptively results inperformances that are theoretically closer to those of anidealistic full-feedback scheme.

• while the general behaviors/trends of the average per-centage of decoded frames and the average PSNR aresimilar with respect to Nt , the effect of different numberof layers for some values of Nt are different. This isdue to the fact that in calculating η, a contribution ofzero is considered to the performance metric if a layer isnot decoded, whereas for the PSNR, error concealment,i.e., showing a decoded frame instead of a lost frame,contributes to the PSNR.

C. Results for Real Video Streams – Multi-User Case

In this subsection, we assess the performance of the pro-posed feedback-free RLNC scheme for the multi-user case.The assessment setup is similar to the previous subsection,i.e., the schemes to be tested are first designed for each GOPand are then tested under some simulated erasure patterns.However, it is required that an aggregate performance function


Fig. 9. Histograms showing the difference of ηtot between feedback-free schemes with optimum and fixed number of layers, for a 3-user case using Foremantest stream. Positive �ηtot values correspond to higher ηtot values of the opt-layer scheme.

H (·) is specified. Here, we first consider a general linearfunction to combine performances of users and compare thefeedback-free and full-feedback schemes. Then, we focus onthe mean and fairness [42] of users’ performances as morespecific aggregate functions and combine them to show theperformance trade-offs. Foreman test stream is used through-out this subsection.

1) General Case: As mentioned previously, to design atransmission scheme for multiple users, various aggregateperformance metrics are possible. Here, in order to makea thorough comparison between the feedback-free RLNCand idealistic full-feedback schemes, we consider a series ofaggregate functions, i.e., we define H (·) as follows

H (z1, . . . , zNu ) =Nu∑

i=1

wi zi (20)

and use various weight vectors W = [w1, . . . , wN ], suchthat

∑Nui=1 wi = 1. The input argument zi is replaced by ηi

and Gsingle(si) for feedback-free and full-feedback schemes,respectively.

Due to the computational complexities of MDP for verylarge state spaces, we limit our study in this section to Nu = 3users and maximum L = 3 layers. Packet error rates areassumed to be Pe1 = 0.1, Pe2 = 0.15 and Pe3 = 0.2 andthe weights wi are chosen from {0, 1/3, 2/3, 1}, which resultin 10 unique weight vectors. We obtain the optimal policiesby using (13), (14) and (17) for each GOP and different Nt

values and then test the designed policies for random erasurepatterns corresponding to each user. This process is repeated100 times for each of the 10 weight vectors. Moreover, fixednumber of layers (1, 2 and 3) and also optimum number oflayers are considered.

The first results, depicted in Fig. 9, reveal the effect ofchoosing the number of layers adaptively for each GOP.The histograms show in what percentage of the cases opt-layerscheme improves the theoretical performance metric for thefeedback-free RLNC scheme. �ηtot in x-axis is defined asthe difference of ηtot between the opt-layer and fixed layerschemes, where positive values correspond to higher ηtot of theopt-layer schemes, negative values correspond to higher ηtot

of the fixed layer schemes and �ηtot = 0 signifies that theopt-layer and fixed layer schemes perform similarly.

It is observed that the proposed opt-layer scheme that selectsthe optimum number of layers for each GOP based on theanalytical results, outperforms the schemes with fixed numberof layers in simulation. Similar to the results for the single-usercase, the amount of improvement varies based on Nt andalso L, and diminishes as Nt gets larger.

Next, we focus on the opt-layer approach and providethe results for the comparison of ηtot values betweenthe feedback-free and the idealistic full-feedback schemesin Fig. 10. We use histograms again and �ηtot for x-axis.Here, positive values of �ηtot correspond to higher ηtot ofidealistic full-feedback schemes and negative values corre-spond to higher ηtot of feedback-free schemes (note that thedefinition and the depicted range of values for �ηtot aredifferent in Figs. 9 and 10.)

From the results, it is interesting to note that even in theworst case of Nt = 13, the feedback-free scheme worksvery similar to the idealistic scheme in more than 80% ofthe cases (when �ηtot = 0). As the possible number oftransmissions Nt increases, the two schemes work even closer.The reason behind this is understandable from the resultsin Fig. 5, where for large Nt values, the opt-layer is in factthe 1-layer approach, which is identical for the feedback-freeand full-feedback schemes.

By repeating the above experiments with lower andhigher sets of PER values, results very similar to thosein Figs. 9 and 10 are obtained, which confirms the robustnessof our proposed schemes.

In addition to the theoretical performance metric, we alsocompare the PSNR of different schemes. To this end, we con-sider the simulation setup mentioned above, but focus on acase where users have equal importance, i.e w1 = w2 =w3 = 1/3, which means the transmission policies are designedbased on the mean theoretical performance metric. We testthe designed policy for each GOP and for each user andrepeat this 100 times to obtain the average PSNR, whichare shown in Fig. 11. The results confirm that the opt-layer feedback-free scheme works very close to the idealisticfull-feedback scheme. In fact, by using adaptive selection ofnumber of layers for each GOP, not only the performanceof the feedback-free scheme is improved, but also the gapwith the idealistic scheme reduces. For the 2-layer and 3-layer


Fig. 10. Histograms showing the difference of ηtot between feedback-free and full-feedback schemes (both with optimum number of layers) for a 3-usercase using Foreman test stream. Positive �ηtot values correspond to higher ηtot values of full-feedback scheme.

Fig. 11. Average PSNR for the multi-user feedback-free and idealisticfull-feedback schemes. Results for opt-layer and 2-layer cases are shown.PSNR values are averaged over the 38 GOPs, the 100 repetitions and the3 users.

cases, the maximum difference in the average PSNR was1.06 and 1.29 dB, which is reduced to 0.72 dB with adaptiveselection of number of layers.

2) Performance Trade-Offs: In this subsection, the purposeis to highlight the trade-offs between the performances ofusers with different channel conditions for the feedback-freeschemes. A simple example of performance trade-off wasshown in Fig. 6 for a two-user case by considering only onesample GOP and the theoretical results were provided. Here,we study a more comprehensive case by considering Nu = 10users and real video test streams, and present the simulationresults.

With the considered number of users, it is not possi-ble to show the performance trade-offs in Nu dimensions.Instead, we consider two aggregate performance functions andstudy their values in 2 dimensions. We use the function definedin (20) and select all the weights to be 1/Nu , so that themean performance is calculated. This is referred to as H1(·).For the second function, we use the Jain’s fairness index [42],which is defined as follows

H2(z1, . . . , zNu ) = (∑Nu

i=1 zi )2

Nu .∑Nu

i=1(z2i )

(21)

with values ranging from 1/Nu (worst case: only one ofthe input arguments is nonzero) to 1 (best case: all theinput arguments are equal). Considering ηi ’s as the input

arguments, maximizing this fairness index leads to designing afair policy in the sense that all users achieve similar theoreticalperformances, regardless of their channel conditions.

Having defined the two aggregate functions, the problemof optimizing their values is a bi-objective optimization.Since, an optimal solution (i.e., a feedback-free transmis-sion policy here) that can maximize both objectives concur-rently may not be found in all cases, we obtain the Paretooptimal solutions and study the trade-off between the twoobjectives. The most common technique to do this is theweighted sum method [43], which combines the objectives asfollows

ηtot = H (η1, . . . , ηNu ) = λH1(η1, . . . , ηNu )

+ (1 − λ)H2(η1, . . . , ηNu ) (22)

Using this ηtot in (14), for every value of 0 ≤ λ ≤ 1,a Pareto optimal solution is obtained [43]. Selecting 51 valuesfor λ from [0, 1] with step size of 0.02, the trade-off curvesin Fig. 12 are resulted.

For the results shown, we have considered the PERs ofusers to be Pei = (i + 1) × 0.05 for 1 ≤ i ≤ 5 andPei = (i − 4) × 0.05 for 6 ≤ i ≤ 10, and similar tothe previous subsections, we have generated random erasurepatterns corresponding to these PERs and then obtained thesimulation results. Furthermore, to investigate mismatch cases,we have also considered optimizing the schemes with a lowerset of PER values (Pei = (i) × 0.05 for 1 ≤ i ≤ 5 andPei = (i − 5) × 0.05 for 6 ≤ i ≤ 10) and then obtainedthe simulated results with the higher PER values mentionedabove.

Simulations for each GOP and each λ are repeated 50 timesand the averages are presented. The main observations aresummarized as follows

• trade-offs between the average percentage of decodedframes and the fairness are evident for different parame-ters. The trade-offs show that selecting the operating pointbased on maximizing the average percentage of decodedframes does not lead to the fairest possible policy, but afairer policy can be chosen at the expense of reducing theaverage percentage of decoded frames.

• the advantage of selecting the number of layers adaptivelyover fixed layer approaches can be observed in Fig. 12(a).For instance, for Nt = 16, fairness of 0.7 is achievedin the opt-layer approach with average percentage ofdecoded frames of 0.5, where the same fairness for the


Fig. 12. Trade-off curves, (a) highlighting the advantage of opt-layer approach for the feedback-free RLNC scheme (b) comparing the feedback-free RLNC,uncoded schemes and mismatch cases. Results for three values of Nt are provided.

4-layer approach is achieved with average percentage ofdecoded frames of 0.33, i.e., around 50% improvementis gained.

• results for the mismatch cases reveal the robustness ofour proposed approach to changes in PER values. In fact,if the feedback-free scheme is optimized for a givenset of PERs and then in another scenario users havehigher PERs, it is not always necessary to re-optimizethe scheme with new PERs, as performance degradationcan be very small and negligible.

• Fig. 12(b) clearly shows that the feedback-free RLNCoutperforms the uncoded scheme.

Note that for the 1-layer case, there is only one option fortransmission, i.e., coded packets from the first layer, hence allthe different values of λ resulted in the single point, which isshown in Fig. 12(a) for each Nt .

VII. CONCLUSION AND DISCUSSION

Network coding combination with unequal error protectionhas shown to be a promising choice to enhance streamingof layered video [14]–[16], [18]. However, there are stillsome knowledge gaps before this technique can be readilyapplied in practice. In this study, we focused on feedback-freeUEP+RLNC and studied some of the unaddressed issues formulti-user broadcasting of layered video over heterogeneouserasure channels. In particular, we contributed by investigatingthe benefits of layered approach for multi-user video stream-ing, comprehensively studying the effect of number of videolayers on the broadcast system design and quantifying the per-formance degradation due to not using feedback. The resultsshow that the proposed feedback-free approach that uses adap-tive selection of number of video layer performs very closeto the idealistic full-feedback system and thus is a promisingcandidate to enhance streaming of layered video in practice.

Although we focused only on the temporal scalability in thesimulations, our proposed framework in this paper is generaland can be easily applied to spatial and quality scalabilityas well. In fact, the main assumptions are that the video is

layered and the importance of each layer can be defined, e.g.,by using (7) or in a similar way as in Remark 4. A similarconclusion applies to the usage of the general aggregatefunction. While we used some basic aggregate functions, it ispossible to consider more complicated aggregate functionsto study our proposed layered approach for various multi-user scenarios. For instance, if users have different displaysand are hence interested in different number of video layers(and consequently different spatial and/or temporal quality),it is possible to define the aggregate function such that thetheoretical performance of each user is limited to what itsdevice can support. Therefore, our study, with some minormodifications, can be used when heterogeneity in device typesexists.

One future research direction is to extend the exist-ing approach to transmission of multiple layered videostreams, where some preliminary results are presented in [44].Moreover, investigating variants of the proposed MDP-basedidealistic scheme to be used in practice (e.g., by incorporat-ing buffering delay and feedback delay [45], [46], utilizingdelayed information in MDP or studying ways to reduce thecomputational complexity) and considering other heterogene-ity cases (e.g., different network topology types or differ-ent mobility conditions for users) are other possible futureresearch directions.

APPENDIX AFINITE HORIZON MDP

A Markov decision process (MDP) [21] is defined with fourmain components as the inputs:

• finite state set S,• finite action set A,• transition probability function P(s|s, a), which shows the

probability of going to state s ∈ S after taking actiona ∈ A in state s ∈ S,

• reward function R(s, a), which shows the immediatereward caused by taking action a ∈ A while in state s ∈ S,

and two components as the outputs:


• policy π(s) that shows the optimum action for anypossible state s ∈ S,

• value function Vπ(s), which is a measure of the expectedreward accumulated by policy π(s).

In the finite horizon MDP, the number of decisionstages (also called horizons, denoted by T ) are limited, hencethe outputs depend on the number of stages-to-go, denoted byt ≤ T , as well. Therefore the notation for the policy and valuefunction should be updated as π(s, t) and V t

π(s), respectively.Moreover, there is a reward at the final stage (i.e., t = 0),which is called the terminal reward. This is another inputcomponent for finite horizon MDP and is denoted by G(s),which represents the reward if the MDP is in state s at thefinal stage.

Having defined all the input components, it is shown thatthe optimal policy and value function for each state s ∈ S canbe recursively obtained by the backward induction method asfollows [21]

V tπ(s) = max

a{R(s, a) +

∑

s∈S

P(s|s, a)V t−1π (s)} (A.1)

π(s, t) = arg maxa

{R(s, a) +∑

s∈S

P(s|s, a)V t−1π (s)} (A.2)

where 1 ≤ t ≤ T and V 0π (s) = G(s). In fact, the optimization

starts with the case of t = 1, where there is no future action,and V 1

π (s) and π(s, 1) are obtained for all the states s ∈ S.Then, it continues for t = 2 and subsequently for othert <= T values, till the optimized policies for all the statesand horizons are acquired. This method is shown to have timecomplexity of O(T |A||S|2) [21].

APPENDIX BUNCODED SCHEME

In the uncoded scheme, it is assumed that out of total Nt , nt�

transmissions are dedicated to the k� packets of the �-th layerin a Round Robin manner such that

∑L�=1 nt

� = Nt . Packetsare transmitted uncoded and NT = [nt

1, nt2, . . . , nt

L ] is decidedin advance, i.e., the scheme is feedback-free.

Assuming b� = � nt�

k� , it can be inferred that c� = nt

� − b�k�

packets are transmitted b�+1 times and the remaining k� − c�

packets are transmitted b� times. Therefore, p�(k�, nt�)=

(1− Pb�e )k�−c�(1− Pb�+1

e )c� is the probability that all the pack-ets of the �-th layer can be delivered successfully. Now, bear-ing in mind that packets of the �-th layer are useful only ifpackets of all the lower layers are received, the probabilityP�(K, NT), defined in Section III-A, will be obtained asfollows

P�(K, NT)

={

(1 − p�+1(k�+1, nt�+1))

∏�j=1 p j (k j , nt

j ); � < L∏�

j=1 p j (k j , ntj ); � = L

(B.1)

The above probabilities can be used in (6) to acquire thetheoretical performance metric.

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Mohammad Esmaeilzadeh (S’09) received the B.E.and M.E. degrees in electrical engineering from theUniversity of Tehran, Tehran, Iran, in 2007 and2010, respectively, and the Ph.D. degree in electricalengineering from Australian National University,Canberra, Australia, in 2016. He was a Researchand Development Engineer on a number of real-world digital communications systems from 2006to 2010. He is currently a Research Assistant withAustralian National University. His research interestsinclude wireless communications, network coding,

signal processing, video streaming, and computer vision.

Parastoo Sadeghi (S’02–M’06–SM’07) receivedthe B.Sc. and M.Sc. degrees from Sharif Universityof Technology, Tehran, Iran, in 1995 and 1997,respectively, and the Ph.D. degree from theUniversity of New South Wales, Sydney, Australia,in 2006, all in electrical engineering. From 1997 to2002, she was a Research Engineer and then a SeniorResearch Engineer with the Iran CommunicationIndustries, Tehran, and also with Deqx, Sydney.She has visited various research institutes, includ-ing the Institute for Communications Engineering,

Technical University of Munich, in 2008, and MIT in 2009 and 2013. She iscurrently an Associate Professor with the Research School of Engineering,Australian National University, Canberra, Australia.

She has co-authored over 140 refereed journal or conference papers and abook on Hilbert Space Methods in Signal Processing (Cambridge UniversityPress, 2013). Her research interests are mainly in the areas of network coding,information theory, wireless communications theory, and signal processing.She is currently serving as an Associate Editor of the IEEE TRANSACTIONSON INFORMATION THEORY. She has been a Chief Investigator in a numberof Australian Research Council Discovery and Linkage projects.

Neda Aboutorab (S’09–M’13) received the B.E.degree from the Iran University of Science andTechnology, Tehran, Iran, in 2005, the M.E. degreefrom the Amirkabir University of Technology,Tehran, in 2008, and the Ph.D. degree from theUniversity of Sydney, Sydney, NSW, Australia,in 2012, all in electrical engineering. From 2012 to2015, she was a Post-Doctoral Research Fellow withthe Research School of Engineering, the AustralianNational University, Canberra, Australia. In 2015,she joined the School of Engineering and IT,

University of New South Wales, Canberra, Australia, as a Lecturer.Her research interests include network coding, wireless communications, datastorage systems, compressive sensing, and signal processing.

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