High-rate analysis of source coding for symmetric error channels

In this paper, new results are derived for the high-rate performance of source coding for symmetric error channels (i.e., a channel where all index errors are equally likely) for a large class of distortion measures. Expressions are derived for the expected distortion including the effect of channel errors as the number of quantization levels N gets large. It is shown that the distortion can asymptotically be approximated as the sum of the source quantization distortion and the channel error induced distortion. In addition, the expressions obtained can be used to glean key insights on the relative amounts of source and channel coding necessary to attain a balanced system, i.e., one where neither the distortion caused by the source quantization nor the distortion caused by channel errors dominate the performance. Optimization of the codebook for minimizing the expected distortion is also considered, and theoretical expressions are derived for the optimal point density.