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

1. Multi-Resolution and Multi-Description: A Low SNR PerspectiveS. Jing, L. Zheng and M. Medard ACHIEVEMENT DESCRIPTION STATUS QUO IMPACT NEXT-PHASE GOALS NEW INSIGHTS • 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 • 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 • 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 • 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 • More general channel models in addition to the quasi-static channel and Gaussian noise • The impact of imperfect channel state information at the receiver Distortion-diversity tradeoff better characterizes layered source-channel schemes

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] 8/10/2014 3

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. Motivation (cont.) • 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?

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 8/10/2014 6

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 8/10/2014 7

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 8/10/2014 8

9. Performance Comparison • 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 8/10/2014 9

10. Performance Comparison (cont.) • 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 sufficientto characterize the source-channel interface, ordering of rates also matters 8/10/2014 10