-Channel Symmetric Multiple Descriptions—Part I:

In this two-part paper, we present a new achiev- able rate region for the general -channel symmetric multiple descriptions problem. In Part I, inspired by the concept of maximum-distance separable (MDS) erasure channel codes, we consider a special case of this rate region, where the source is encoded into descriptions each with rate . These descriptions are transmitted over bandwidth constrained and errorless channels. During transmission, a subset of these channels can break down, thus erasing the corresponding descriptions. The decoder is interested in recovering the source with the reception of at least descriptions. Thus, the encoder is allowed to sample only one realization of this breakdown process during the entire transmission. For Gaussian sources, we have the following interesting result: when any descriptions arrive, the achievable distortion exactly matches the optimal distortion-rate performance corresponding to a source rate of bits; with the reception of any de- scriptions, the source reconstruction quality is strictly better, the improvement being nearly linear in the number of descriptions re- ceived.