Sliding-Window Digital Fountain Codes

for Streaming of Multimedia Contents

Matta C.O. Bogino,

Pasquale Cataldi,

Marco Grangetto,

Enrico Magli,

Gabriella Olmo.

IEEE International Symposium on Circuits and Systems (ISCAS), 2007.

Outline

• Introduction

• Proposed Method

• Performance Analysis

• Conclusions

• Future Works

Introduction

• Luby Transform (LT) Codes:– Encoding process

• For the ith encoding symbol (packet), select degree di by Soliton distribution

• Choose di source data

• Perform XOR on chosen data

– Decoding process• Decode degree-one encoded symbols

• Remove degree-one edges iteratively…

x1 x2 x3 x4 x5 x6

y1 y2 y3 y4 y5

x1

x3

x2

x2

x5

x3

x5

x6

Degree 1 2 3 … k

probability Ω1 Ω2 Ω3 … Ωk

x4

Introduction

• Digital Fountain (DF):– Decoder can recover original data from enough

number of received encoded packets.• Any subset of the encoded packets.

– Receive n = (1 + ) · k encoded packets can recover k original data.

• ε: code overhead.

– Digital Fountain Codes are potentially (asymptotically) optimal.

• for k → ∞, such that ε→ 0

Introduction

I I IP Pplayed!

queuedqueuedqueued queued

I I IP PP P P PP P P PP PP P P

Pqueued

discarded!discarded!

• Many applications require short data block length:– k↓, such that ε↑, overhead↑– k ↑, such that ε↓, overhead↓

• Video streaming:

Introduction

• Sliding Fountain (SF):– Use a windowing approach to partition the information

data (original source data).– Encoder chooses source data among those in a

sliding window.• Sliding window moves following the chronological order of

the video stream.

– Provides a rough temporal ordering of the received packets.

• Avoiding expired information to be processed.

Proposed Method

• Sliding Windows:

Proposed Method

• Sliding Windows:

A GB DC E H JI KF L

data streaming (chronological order)

A G MB DC E H JI K N PO QF L R

A D GB DC E E GF H H JI KF I L

A GB DC E H JI KF L

Proposed Method

• Sliding Windows:

– Number of windows that consider a particular symbol: w / s

window movementwindow lengthoverlap region

A G MB DC E H JI K N PO QF L R

w = 6s = 2

Proposed Method

overlap regionwindow movement

A B C D E F G H I J K L

A B C D E F D E F G H I G H I J K L

A B C D E F C D E F G H E F G H I J G H I J K L

s = 3

s = 2

w = 6

• Sliding Windows:– The overlap strategy permits to virtually extend the window

length.

• s↓, such that (w – s)↑, virtual block length↑, ε (overhead)↓.

Proposed Method

• Total overhead:– The total overhead of the SF code is equal to traditional DF.

– Conventional DF encoder:

– SF encoder: • Each source data is processed in w/s windows.

• The number of source data as virtually enlarged:

• The number of encoded packets can be generated, on average, for every virtual source data:

(1 )n

k

'w

k ks

(1 )(1 )

'

n k swk wks

Proposed Method

• Why more efficient?– The number of encoded symbols can be generated from

each window of SF:

– The number of encoded packets that generates in every window of SF code is smaller than traditional DF code in order to recover the whole information.

(1 )wn s (1 )

f

n n ww

N k

<

(1 )wn s

Number of encoded packets generates per window (SF code)

Number of encoded packets generates per window (DF code)

• Total number of windows in DF code: Nf = k / w

Proposed Method

• Why more efficient?– The number of encoded packets that generates in every

window of SF system is smaller than traditional DF code in order to recover the whole information.

8 8

8

88

DF Code:

SF Code:

12 12

8 88

Proposed Method

• SF decoder:– A conventional DF decoder, does not require to know

windowing is being used.

• Two decoding cases:– All the symbols of the window have been solved.

• Usually there are not enough encoded symbols to recover all the window source data.

– There are still unsolved equations.• Decoder requires a suitable amount of memory to store all

the unsolved equations.• Would be solved using the new incoming symbols.

– window overlap.

Performance Analysis

• Using LT Codes to analyze on varying:– Window speed.– Total overhead of the code.

• LT Codes:– Robust Soliton distribution:

• Constant: δ& c were set empirically.

• Performed on an personal computer.– Intel Pentium 4 processor 1.7 GHz– 512 MB of Ram– Linux OS

Performance Analysis

Performance Analysis

Undecoded Symbols as a function of the Received Overhead

Performance Analysis

Simulation Failure Probability as a function of the Received Overhead

Performance Analysis

Encoding Times as a function of the Received Overhead

Performance Analysis

Decoding Times as a function of the Received Overhead

Performance Analysis

Peak of Memory Usage as a function of the Received Overhead

Conclusions

• Presented an innovative Sliding Fountains (SF) transmission scheme.

• The window sliding through the data stream and leaving some overlap between successive steps.– Permits to virtually enlarge block length to obtain high

er code efficiency.

• Keeping the overhead constant, SF approach allows to achieve an undecoded symbol rate lower of 105 than traditional ones.

Conclusions

• Time complexity:– SF encoding process is less complex.

– An increasing of decoding complexity with low values

of ε, where traditional systems cannot work properly.

• SF system needs a lower amount of memory with respect of a traditional one.

Future Works

• The system parameters can be tuned in order to transmit multimedia contents over critical channels.

• SF scheme can be further modified so that an Unequal Error Protection (UEP) can be performed.