•Three-layer scheme dominates previous double-layer schemes

•Distortion-diversity tradeoff provides useful comparison in different operating regions

Layered Source-Channel Schemes: A Distortion-Diversity Perspective: S. Jing, L. Zheng and M. Medard

•Diversity can be achieved through source coding techniques, like multiple description codes

•We characterize source-channel schemes with distortion-diversity tradeoff

Distortion-diversity tradeoff better characterizes layered source-channel schemes

MAIN ACHIEVEMENT:

A three-layer source-channel scheme, which includes previous multi-resolution-based and multi-description-based schemes as special cases

HOW IT WORKS: • Multi-description source code with a common

refinement component

• Superposition coding with successive interference cancellation

• Joint source-channel decoding exploits source code correlation

ASSUMPTIONS AND LIMITATIONS:

• Quasi-static block-fading channel

• Receivers have perfect channel state information, but the transmitter only has statistical knowledge of the channel

•Conventional source-channel scheme achieves a single level of reconstruction

•Diversity is usually achieved in the channel coding component

•Extend multi-description-based source-channel scheme while preserving the interface between source and channel coding

•More general channel model

IMPA

CT

NEX

T-P

HA

SE G

OA

LS

ACHIEVEMENT DESCRIPTION

STA

TU

S Q

UO

NEW

IN

SIG

HTS

Multiple Description

with Common

Refinement

Channel 1

s

ˆpartials

Channel 2

1-D ChannelEncoder (SNR)

1bi

2bi

Joint Source-Channel Decoder1-D Channel

Encoder (SNR)

2-D Channel Encoder

ri+

+

refines

ˆfulls

1 2ˆ ˆ or b bi i

1 2ˆ ˆ, b bi i

1-(SNR )

1x 1y

2x 2y

1bx

1rx

2bx1 2

ˆ ˆ ˆ, , and b b ri i i

2rx

partial

refine full,

4 / 31

1/ 3

7 / 95 / 6

Multi-resolution

Multi-description

Three-layer

Source (Image)

PDA 1

PDA 2

Laptop 1

Laptop 2

PDA 1

PDA 2

Laptop 1

Laptop 2

...010011100......010111100...

...101011011...

Sheng Jing, Lizhong Zheng, Muriel Médard

ITMANET

Mar 2009

Motivation

• Multiple user groups

(eg. PDAs vs. Laptops)

• Accuracy: image resolution

• Reliability: successful image loading probability

• Different preferences of accuracy vs. reliability

• How well can we serve multiple user groups simultaneously?

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Background

• [Diggavi et al ’03]

Layered channel codes (“diversity-embedded codes”)

• [Diggavi et al ’05]

Tradeoff between diversity orders of 2-layer channel code

• [Effros et al ’04] [Laneman et al’05]

Source coding techniques can also improve diversity for certain reconstructions

• We previously looked at the tradeoff between distortion and diversity for SR and MD schemes [Jing et al ’08]

• In this talk, we present a unifying scheme that matches the distortion and diversity (D-D) tradeoff of SR and MD schemes

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Outline

• Problem formulation

• Review of two schemes– SR with superposition coding– MD with joint decoding

• Unifying scheme: MD with common refinement

• Performance comparison

• Concluding remarks

23/4/20 5

Problem Formulation

• Source: i.i.d. unit-variance complex Gaussian

• Quadratic distortion measure

• Quasi-static parallel fading channel

where and

• Power constraint: SNR per subchannel

• No channel state information at transmitter

• Perfect channel state information at receiver

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[ ] [ ] [ ], 1, 2i i i iy n h x n w n i

(0,1)ih CN [ ] (0,1)iw n CN

Problem Formulation (cont.)

• At high SNR, for each source reconstruction

– Distortion exponent:

– Diversity order:

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sˆlog E [ ( , )]

limlogs

SNR

d s sd

SNR

out ˆlog P [ ]lim

logSNR

s

SNR

Problem Formulation (cont.)

• Distortion-Diversity (D-D) tradeoff: achievable distortion exponent & diversity order tuples– Example: three reconstructions (partial, full, and refine),

D-D tradeoff includes all achievable

– Alternative performance metric: average distortion

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( , , , , , )partial partial full full refine refined d d

Two schemes

• SR with superposition coding

• : two-layer successive refinement source code matched to the distortion levels

• : superposition channel code, with power and

• : successive interference cancelation channel decoder

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SNR 1SNR

,partial refineD Ds ( , )b ri i

( , , , )partial partial refine refined d

( , )b ri i 1 2( , )x x

1 2( , )y y ˆ ˆ ˆ or ( , )b b ri i i

Two schemes (cont.)

• MD with joint decoding [Laneman et al ’05]

• : symmetric El-Gamal-Cover (EGC) code [El Gamal et al ’82] matched to distortions

• : joint source-channel decoder– Use correlation between source codewords to

identify unlikely pairs of channel codewords

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1 2( , )i i

( , , , )partial partial full fulld d

s1 2( , )i i

1 2( , )y y1 2 1 2ˆ ˆ ˆ ˆ or or ( , )i i i i

,partial fullD D

Performance Comparison

• SR scheme: D-D tradeoff

along the direction of

• MD scheme: D-D tradeoff

along the direction of

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( , , , )partial partial refine refined d

, 1.5partial refined d d d

( , , , )partial partial full fulld d

, 1.5partial fulld d d d

Performance Comparison (cont.)

• Compare the D-D regions

at

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2 / 3d

Common Refinement Scheme

• : symmetric EGC code with common refinement matched to

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2

2 2,1 ,2

2 2

0 0 0

( , , ) 0 , 0

0 0

r

r b b b b

b b

w w w CN

s ,1 ,2( , , )b b ri i i, ,partial full refineD D D

( , , , , , )partial partial full full refine refined d d

Common Refinement Scheme (cont.)

• Treating refinement layer as noise, form candidate lists of , resp.

• Search for a jointly typical candidate pair – If find only one pair, subtract the corresponding channel

codewords and decode for – Otherwise, search each candidate list for

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,1 ,2,b bi i

ri

,1 ,2,b bi i

,1 ,2 or b bi i

Connection with SR and MD

• Common refinement scheme includes the MD scheme as a special case (set )

• Common refinement also includes SR scheme?– Simple approach requires huge codebook

– We show, makes the common refinement scheme as good as SR in D-D tradeoff, and avoids exploding

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( 1)

1 ( 0)SNR

2 2

,1 ,2 2 2

0( , ) ,

0b b

b b

b b

w w CN

1

bR

11 2 22 ( ; ( ; ), )b b b b bR I s ss s I s

Performance Comparison

• D-D tradeoff: ,

• Extreme case 1:

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( , ) (2 / 3, 1)partial refined d partial full refined d d

full refined d

( , )partial full

( , )partial refine

Performance Comparison (cont.)

• D-D tradeoff: ,

• Extreme case 2:

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( , ) (2 / 3, 1)partial refined d partial full refined d d

full partiald d

( , )partial full

( , )partial refine

Concluding Remarks

• 3-level unifying scheme– Dominates both SR and MD schemes– Smooth transition between SR and MD schemes– No strictly superior performance

• On-going work– Parallel channel MIMO channel– Unifying source-channel scheme that also preserves the

digital source-channel interface

23/4/20 18