1. 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 Perspective S. 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 IMPACT NEXT-PHASE GOALS ACHIEVEMENT DESCRIPTION STATUS QUO NEW INSIGHTS

2. 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

3. 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] 10/17/20153

4. 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

5. 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.)

6. 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 10/17/20156

7. 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 10/17/20157

8. 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 10/17/20158

9. Performance Comparison 10/17/20159 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

10. Performance Comparison (cont.) 10/17/201510 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