Diversity for Parallel Channels to Minimize the Average Distortion

The problem of transmitting a source across a parallel channel with random states only known at the decoder is considered. We focus on minimizing the average distortion. The general problem is unsolved. There are two commonly used architecture, namely source coding diversity and channel coding diversity, which exploit diversity through parallel channel coding or multiple description (MD) source coding. The performance depend on the channel model. Source coding diversity is better for on-off channel models, but for channels with a continuous range of quality, the channel coding diversity is better. In this paper, we provide a joint source-channel coding schemes and a separate coding scheme, both of which have advantage of both channel coding diversity and source coding diversity. Our schemes achieve strictly better performance than MD encoding with joint source-channel decoding introduced by Laneman, et al. Finally, inspirited by Nair, et al., a better coding scheme combining superposition, Gelfand-Pinsker coding, Marton coding, and indirect decoding is given.