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

1. Layered Source-Channel Schemes: A Distortion-Diversity Perspective: S. Jing, L. Zheng and M. Medard ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS • Three-layer schemedominates previous double-layer schemes • Distortion-diversity tradeoff provides useful comparison in different operating regions • 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 • Diversity can be achieved through source coding techniques, like multiple description codes • We characterize source-channel schemes with distortion-diversity tradeoff • Extend multi-description-based source-channel scheme while preserving the interface between source and channel coding • More general channel model Distortion-diversity tradeoff better characterizes layered source-channel schemes

2. Layered Source-Channel Schemes Sheng Jing, Lizhong Zheng, Muriel Médard ITMANET Mar 2009

3. 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?

4. 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

5. 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

6. 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

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

8. 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

9. 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

10. 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

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

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

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

14. 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

15. 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

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

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

18. 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