•MD-based scheme could outperform MR-based scheme while preserving the source-channel interface

•Rate is not sufficient as source-channel interface, ordering of rates also matters

Multi-Resolution and Multi-Description: A Low SNR PerspectiveS. Jing, L. Zheng and M. Medard

•MR provides multiple layers of bit sequences without any loss from the rate-distortion perspective

•MD provides us with the flexibility of decoding order while suffering from certain rate-distortion loss

•MR is a perfectly good source code for the high-resolution case, while MD may be advantageous in the low resolution scenario

•Certain elements may be missing from the traditional source-channel interface

Distortion-diversity tradeoff better characterizes layered source-channel schemes

MAIN ACHIEVEMENT:An example demonstrating that the multi-description scheme could outperform the multi-resolution scheme while preserving the source-channel interface.

HOW IT WORKS: • 2x1 MIMO channel in the low SNR regime as

SNR approaches zero• The usual multi-resolution scheme using super-

position channel coding• Multi-description based scheme does not use a

joint the source-channel decoder.

ASSUMPTIONS AND LIMITATIONS:• Quasi-static block-fading channel• Receivers have perfect channel state information,

but the transmitter only has statistical knowledge of the channel

•We have proposed the framework of distortion-diversity tradeoff as a new performance metric to study source-channel schemes

•We demonstrated the advantage of MD-based scheme over MR-based scheme if joint source-channel interface is not preserved

•We further proposed an innovative three-layer source-channel scheme, which smoothly connects the MD-based and the MR-based schemes

•More general channel models in addition to the quasi-static channel and Gaussian noise•The impact of imperfect channel state information at the receiver

IMPA

CTNE

XT-P

HASE

GOA

LS

ACHIEVEMENT DESCRIPTION

STAT

US Q

UONE

W IN

SIGH

TS

PDA 1

PDA 2

Laptop 1

Laptop 2

...010011100...Multiple

Descriptions

1xy partials

2x

1-D ChannelEncoder1i

2iSeparate Decoder

1-D ChannelEncoder

SourceReconstruct

fullsSource

Reconstruct

1 2ˆ ˆ or i i

1 2ˆ ˆ, i i

...

...

Motivation

• Wireless broadcast network with multiple user groups (PDAs, Laptops)– Application: image/video distribution– Accuracy: image/video resolution– Reliability: probability of successful image/video loading– Different user groups require different accuracy-reliability tradeoff– How to accommodate multiple user groups simultaneously?

• Source coding approaches– Multiple coded messages, intended for different user groups– Multi-resolution (MR): a sequence of coded messages– Multi-description (MD): multiple parallel coded messages

Motivation (cont.)

• Source coding approaches (cont.)– MR successively refine the rate-distortion tradeoff for certain cases (most

noticeably, Gaussian source + quadratic distortion)– MD provides more flexibility in the ordering of coded messages

• Channel coding approaches– Diversity-embedded channel codes [Diggavi et al ’03] – For channels of 1 degree of freedom (SISO, SIMO, MISO), the diversity-

multiplexing tradeoff is successively refinable [Diggavi et al ’05]

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Motivation (cont.)

• Channel coding approaches (cont.)– For channels of 1 degree of freedom, optimal channel code is superposition code

(SPC), decoded by successive interference cancelation (SIC)

– However, for channels of more than one degree of freedom, the diversity-multiplexing tradeoff is not successively refinable [Diggavi et al ’06]

• Source-channel schemes– MR naturally matches with SPC (MR-SPC), base message encoded into base layer,

refinement message encoded into refinement layer– MD-based scheme (MD-JD) uses a joint source-channel decoder [Laneman et

al’05] – How does MR-SPC compare with MD-JD performance-wise?– We have proposed the distortion-diversity tradeoff as our performance metric

• Source-channel schemes (cont.)– Traditional performance metric is average (over both source randomness and

channel randomness) distortion– Average distortion metric is not appropriate for delay-limited applications– MR-SPC and MD-JD achieve the same average distortion exponent [Laneman et

al’05]

• Distortion-diversity tradeoff– Characterize the relationship between distortion and outage probability– We are able to compare MR-SPC and MD-JD in a finer resolution– We have proposed a three-layer scheme that unifies MR-SPC and MD-based

scheme in our distortion-diversity framework

• Source-channel interface– Both MR and MD encode source into two bit streams– MR incurs no loss in terms of rate-distortion tradeoff– However, MD-based scheme could still outperform MR-based scheme (in low SNR

regime) in terms of distortion-diversity tradeoff– Is bit rate a complete source-channel interface?

Motivation (cont.)

Low SNR Problem Formulation

• Quasi-static 2x1 MIMO channel

where and

• Power constraint: SNR per transmit antenna

• No channel state information at transmitter

• Perfect channel state information at receiver

• At low SNR, we consider the constant outage probability case: for each reconstruction– Diversity order:– Distortion coefficient:

• Distortion-diversity (D-D) tradeoff: achievable distortion coefficient and diversity order tuples

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1 1 2 2[ ] [ ] [ ] [ ]y n h x n h x n w n

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

s

0

ˆ1 E [ ( , )]lim s

SNR

d s sd

SNR

ˆP[ ( )]O s

( , , , )partial partial full fulld d

MR-based Scheme

• : multi-resolution source code matched to distortion levels

• : superposition channel code, with power and , which achieves the same rate as the Alamouti code

• : successive interference cancelation channel decoder

• D-D tradeoff: achievable

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SNR(1 )SNR

,partial refineD Ds ( , )b ri i

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

y ˆ ˆ ˆ or ( , )b b ri i i

( , , , )partial partial refine refined d

MD-based Scheme

• MD with separate decoding

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

• : separate decoder– Use the sub-sequence of that corresponds to active

transmit antenna 1 to decode for – Similarly, decode for – If both and are decoded, output ; otherwise, if

either or is decoded, output

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1i

( , , , )partial partial full fulld d

s1 2( , )i i

y1 2 1 2ˆ ˆ ˆ ˆ or or ( , )i i i i

,partial fullD D

y

2i1i 2i ˆfulls

1i 2i ˆpartials

Performance Comparison

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• We compare 2-dimensional cuts of the D-D tradeoff – Case 1: and (left figure)– Case 2: and (right figure)

• Even with separate decoding, MD still outperforms MR in certain operational regions

– When outage probability is low (case 1), MR-SPC outperforms MD-SD – When outage probability is high (case 2), MD-SD outperforms MR-SPC

0.16partial ( , )partial fulld d

0.64full 0.64partial 0.96full

Performance Comparison (cont.)

04/22/23 10

• MR-SPC seems should be optimal in our setting– MR incurs no loss in terms of rates, for given distortion levels– SPC successively refine the diversity-multiplexing tradeoff for 2x1 MIMO

channel

• However, MR-SPC is still defeated in certain cases– MR restrict a particular decoding order, while MD offer flexibility– Rate is not sufficient to characterize the source-channel interface, ordering

of rates also matters