A new achievable region for Gaussian multiple descriptions based on subset typicality

This paper addresses the L-channel multiple descriptions problem for a Gaussian source under mean squared error (MSE) distortion metric. We focus on particular cross-sections of the general rate-distortion region where a subset the 2L - 1 distortion constraints are not imposed. Specifically, we assume that certain descriptions are never received simultaneously at the decoder and thereby the transmitted codewords require joint typicality only within prescribed subsets. We derive a new encoding scheme and an associated rate-distortion region wherein joint typicality of codewords only within the prescribed subsets is maintained. We show that enforcing joint typicality of all the codewords entails strict suboptimality in the achievable rate-distortion region. Specifically, we consider a 3 descriptions scenario wherein descriptions 1 and 3 are never received simultaneously at the decoder and show that a strictly larger achievable region is obtained when the encoder maintains joint typicality of codewords only within the required subsets. To prove these results, we derive a lemma called the `subset typicality lemma' which plays a critical role in establishing the new achievable region.