opportunistic network communications

ÉCOLE POLYTECHNIQUEFÉDÉRALE DE LAUSANNE

Overview Data vs voice Opportunistic source coding Discussion

Opportunistic network communications

Suhas Diggavi

School of Computer and Communication SciencesLaboratory for Information and Communication Systems (LICOS)

Ecole Polytechnique Fédérale de Lausanne (EPFL)Lausanne, Switzerland

Email: {chao.tian,suhas.diggavi}@epfl.chURL: http://licos.epfl.ch

August 31, 2006

Joint work with David Tse (Berkeley) and Chao Tian (EPFL)



Opportunism in communications

Uncertainty is inherent in network communications.

Randomness in channel/transmission conditions.

Variations in QoS requirements of traffic.

Diverse receiver state information.

A conservative strategy is to design for worst case.

An opportunistic strategy tries to utilize the randomness toenhance overall performance.

Question: How do we utilize uncertainties opportunistically?

We examine two illustrative applications:

Wireless communication.

Multi-terminal source coding.



Fading wireless channels

Observation: Wireless channels are inherently random.

Implications:

Channels can sometimes be very weak (deep “fade”).

Transmitter may not be able to track the channel.

Channel models:

Quasi-static fading channel =⇒ random but constant incoding block.

Receiver channel knowledge, no knowledge at transmitter.

Question: Can we opportunistically use channel randomnessto our advantage?



Data versus voice

Two approaches to provide reliability:

Delay-tolerant traffic (data):

Re-transmissions correct errors.

Rate can be aggressively choosen based on averagechannel.

Real-time traffic (voice):

Need to get it right “first” time.

To be designed to succeed even in deep fades =⇒ highreliability.



Segregate or aggregate?

Modern wireless networks carry both real-time anddelay-tolerant traffic.

A natural solution is to segregate them on orthogonalresources (different time-slots, frequency-slots etc.).

We show that there is a performance advantage toaggregating them on the same resource.

Advantage comes because of diverse QoS requirementsand opportunistic use of random wireless channels.



Rate versus reliability (diversity)

Diversity order: If averageerror probability is Pe(SNR),diversity order d is,

limSNR→∞

log(Pe(SNR))

log(SNR)= −d

=⇒ Pe(SNR) ≈ SNR−d

Multiplexing rate r : Transmission rate R(SNR) = r log(SNR).

Question: Is there a tension between rate and reliability?



Rate versus reliability (diversity)

Diversity order: If averageerror probability is Pe(SNR),diversity order d is,

limSNR→∞

log(Pe(SNR))

log(SNR)= −d

=⇒ Pe(SNR) ≈ SNR−d Log

Err

or P

roba

bilit

y

d

SNR (dB)

2d

1

Multiplexing rate r : Transmission rate R(SNR) = r log(SNR).

Question: Is there a tension between rate and reliability?



Rate-diversity trade-off (Zheng and Tse, 2003)

r(min(M , M ),0)

RateMultiplexing

GainDiversity

t

t

t(1 , (M−1)(M−1))

(k , (M −k)(M −k))

r

t r(0 , M M )

r

.

.

.

.

.

.

Interpretation: Formultiplexing rate k , it is likeusing Mr − k receive antennasand Mt − k transmit antennasto provide diversity.

Establishes rate-reliability trade-off for fading channels forsingle traffic type.



Data versus voice: Formulation

Goals: We want to guarantee

A multiplexing rate rV for voice with reliability (diversity) ofd .

A multiplexing rate rD for data with positive diversity order.

Questions:

For given d what is the best achievable (rV , rD)?

Is it achievable through segregation?



Opportunistic coding

Classical setting: Singlerate-reliability (outage) point.

Rate-outage pair: Recovermessage m with reliabilityp = P {O}. Characterizeachievable (R, p) pair.

m

O

|h|2

O

Recover message

Consequence: Loseopportunity to transmit athigher rate for better channels.



Opportunistic coding

Classical setting: Singlerate-reliability (outage) point.

Rate-outage pair: Recovermessage m with reliabilityp = P {O}. Characterizeachievable (R, p) pair.

m

O

|h|2

O

Recover message

Consequence: Loseopportunity to transmit athigher rate for better channels.

Opportunistic coding: mV

recovered if H ∈ OV and(mV , mD) to be recovered ifH ∈ G.

��

|h|2

OV

mV (mV , mD)

OV G

Rate-outage tuple: MessagemV has outage probabilitypV = P {OV} and mD hasoutage pD = P

{G}

.Goal: Characterization ofachievable (RV , pV , RD, pD)tuples.



Mt × 1, Rayleigh fading channel

��

��

Extra region for aggregated��

��

��

��

Segregated

��

rD

rV ≤ 1 −d

Mt

rV + rD ≤ 1

rV

Superposition encoding for aggregated traffic with i.i.d.Gaussian codebooks.Broadcast approach (Cover ’72, Shamai ’97) for averagerate behavior.Focus here on rate-reliability trade-off.



Mixing traffic typesLessons from social structure?

Similar results holds for multiple degrees of freedom (parallelchannels, MIMO channels).

Lessons:

Aggregation is better than segregation.

Gain comes from mixing traffic with different QoSrequirements

Opportunistic use of random channel variation to pushthrough delay tolerant traffic.



Opportunistic source coding

Scalable delivery of source to multiple decoders.

Opportunistic source coding robust to uncertain decoderside-information.



Progressive encoding with decoder side-information

ENCODERStage 1

Stage 2

Source

Decoder 2

Decoder 1

Y2(k)

X1(k)

X2(k)

i1 ∈ IM1

{X(k)}

i2 ∈ IM2

ψ1(y1, i1)

ψ2(y2, i1, i2)

Y1(k)

Side-information quality

Side-information quality is modeled by “degradedness” ofside-information.

Side-information scalable coding: Lower-delay deliveryfor decoder with better side-information, X ↔ Y1 ↔ Y2 =⇒side information deteriorates with stages.



Side-information scalable source coding

Problem set-up: First stage has better “quality”side-information, X ↔ Y1 ↔ Y2.

Goal: Allow decoder with better side-information to decodewith smaller delay.

Heegard-Berger rate-distortion function (1985): IfX ↔ Y1 ↔ Y2, lower bound on total rate needed:

RHB(D1, D2) = minp(D1,D2)

[I(X ; W2|Y2) + I(X ; W1|W2, Y1)]

where (W1, W2) ↔ X ↔ Y1 ↔ Y2.Questions:

Can we describe information that is maximally useful toboth decoders?

How much do we lose due to progressive requirement?



Coding scheme: Basic idea

Refinement for decoder 1

Coarser bins

Finer bins

Binning for V1 3 42

1

Binning for W1

Coarse bin 1Enumerate to finer bin 4

Binning for W2

NESTEDBINNING

Refinement for decoder 2

The first stage encodes V using binning for decoder 1 torecover using Y1. Also refinement W1 if needed.

The second stage enumerates for decoder 2 to recover Vusing Y2. Also refinement W2 if needed.



Achievable rate-region Rach(D1, D2)

1 (W1, W2, V ) ↔ X ↔ Y1 ↔ Y2.2 There exist deterministic maps fj : Wj × Yj → X such that

Ed(X , fj(Wj , Yj)) ≤ Dj , j = 1, 2.

3 The non-negative rate pairs satisfy:

R1 ≥ I(X ; V , W1|Y1)

R1 + R2 ≥ I(X ; V , W2|Y2) + I(X ; W1|Y1, V ).

Interpretation:

R1 ≥ I(X ; V , W1|Y1) = I(X ; V |Y1)︸︷︷︸

coarse bin

+ I(X ; W1|Y1, V )︸︷︷︸

Decoder 1 refinementR2 ≥ I(V ; Y1|Y2)

︸︷︷︸

enumerate to finer bin

+ I(X ; W2|Y2, V )︸︷︷︸

Decoder 2 refinement



Gaussian example: A complete characterization

Source: Gaussian i.i.d. source, X ∼ N(0, σ2x )

Distortion measure: Quadratic error, E[|X − X |2] ≤ D.

Side-informations: N1, N2 are independent Gaussians,SI-scalable: Y1 = X + N1, Y2 = X + N1 + N2

Result

Wyner-Ziv bound in first stage and Heegard-Berger sum ratebound are both simultaneously achievable.

Implication: This is the best one could have hoped for, andthere is no loss in opportunistic transmission.



Mixture of receiver side-informationsCharacterization of optimal strategies

Formulation of side-information scalable coding.

Opportunistically serve better receivers while maximallyutlizing information for others.

Complete characterization for Gaussian sources.

Open questions:

Characterization for arbitrary sources: only inner and outerbounds found.

Characterize loss due to progressive description.



Conclusions

There are many other aspects of network communication whereopportunism has been used, e.g., opportunistic scheduling.

Main message: Randomness inherent in networkcommunications can be utilized to develop opportunisticstrategies.Open questions:

Complete characterization of rate-diversity tuples foropportunistic coding for wireless.

Impact of this availability of such links for improvingend-to-end performance.

Complete characterization of rate-distortion tuples foropportunistic multi-terminal source coding.

opportunistic network communications

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