Optimized Analog Mappings for Distributed Source-Channel Coding

This paper focuses on optimal analog mappings for zero-delay, distributed source-channel coding. The objective is to obtain the optimal vector transformations that map between m-dimensional source spaces and k-dimensional channel spaces, subject to a prescribed power constraint and assuming the mean square error distortion measure. Closed-form necessary conditions for optimality of encoding and decoding mappings are derived. An iterative de- sign algorithm is proposed, which updates encoder and decoder mappings by sequentially enforcing the complementary optimality conditions at each iteration. The obtained encoding functions are shown to be a continuous relative of, and in fact subsume as a special case, the Wyner-Ziv mappings encountered in digital distributed source coding systems, by mapping multiple source intervals to the same channel interval. Example mappings and performance results are presented for Gaussian sources and channels.