Combinatorial Message Sharing for a refined multiple descriptions achievable region

This paper presents a new achievable rate-distortion region for the L-channel multiple descriptions problem. Currently, the most popular region for this problem is due to Venkataramani, Kramer and Goyal [3]. Their encoding scheme is an extension of the Zhang-Berger scheme to the L-channel case and includes a combinatorial number of refinement codebooks, one for each subset of the descriptions. All the descriptions also share a single common codeword, which introduces redundancy, but assists in better coordination of the descriptions. This paper proposes a novel encoding technique involving `Combinatorial Message Sharing', where every subset of the descriptions may share a distinct common message. This introduces a combinatorial number of shared codebooks along with the refinement codebooks of [3]. These shared codebooks provide a more flexible framework to trade off redundancy across the messages for resilience to descriptions loss. We derive an achievable rate-distortion region for the proposed technique, and show that it subsumes the achievable region of [3].