Erasure Multiple Descriptions

A binary erasure version of -channel multiple descriptions (MD) with symmetric descriptions (i.e., the rates of the descriptions are equal and the distortion constraint depends only on the number of messages received) is considered. No excess rate for every out of descriptions, i.e., any messages have sum rate , where is Shannon's rate-distortion function for erasure distortion and is the distortion constraint to be met, is investigated. The goal is to characterize the achievable distortions . Reconstruction fidelity is measured using two criteria: a worst-case criterion which computes distortion by maximizing the per-letter distortion over all source sequences, and an average-case criterion which computes distortion by averaging the per-letter distortion over all source sequences. Achievability schemes are presented, based on systematic maximum distance separable codes for worst-case distortion and random binning for average-case distortion, and optimality results are proved for the corresponding distortion regions. The erasure MD setup is then used to propose a layered coding framework for multiple descriptions, which is then applied to vector Gaussian MD and shown to be optimal for symmetric scalar Gaussian MD with two levels of receivers and no excess rate at the central receiver.