n-channel multiple descriptions: theory and constructions

We present new achievable rate regions and code constructions for the symmetric n-channel multiple descriptions (MD) coding problem (Puri et al. (2002)) for n>2. Our approach is inspired by unexplored connections between MD and the problem of distributed source coding (Slepian et al. (1973); Wyner et al. (1976)). For illustrative clarity, we restrict our focus to the important special case relating to (n, k) source-channel erasure codes (Pradhan et al. (2001)). This involves n encodings of a source with the goal of maximizing its reconstruction fidelity with the availability of any k of them, while strictly improving this reconstruction fidelity with the availability of more than k descriptions. We describe the underlying information-theoretic framework, and then formulate practical constructions based on scalar quantizers and linear channel codes for the n=3 case to illustrate our concepts.