md-based scheme could outperform mr-based scheme while preserving the source- channel interface rate...
TRANSCRIPT
•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
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ACHIEVEMENT DESCRIPTION
STA
TU
S Q
UO
NEW
IN
SIG
HTS
PDA 1
PDA 2
Laptop 1
Laptop 2
...010011100...Multiple
Descriptions
1x
y partials
2x
1-D ChannelEncoder1i
2i
Separate 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.)
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• 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