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 IMPACT NEXT-PHASE GOALS ACHIEVEMENT DESCRIPTION STATUS QUO NEW INSIGHTS

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?

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

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

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

Problem Formulation (cont.) At high SNR, for each source reconstruction –Distortion exponent: –Diversity order:

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

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

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

Performance Comparison SR scheme: D-D tradeoff along the direction of MD scheme: D-D tradeoff along the direction of

Performance Comparison (cont.) Compare the D-D regions at

Common Refinement Scheme : symmetric EGC code with common refinement matched to

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

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

Performance Comparison D-D tradeoff:, Extreme case 1:

Performance Comparison (cont.) D-D tradeoff:, Extreme case 2:

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