Source Coding for Multiple Descriptions II: A Binary Source

Abstract

A uniformly distributed (iid) binary source is encoded into two binary data streams at rates R 1 and R 2 , respectively. These sequences are such that by observing either one separately, a decoder can recover a good approximation of the source (at average error rates D 1 , D 2 , respectively), and by observing both sequences, a decoder can obtain a better approximation of the source (at average error rate D 0 ). In this paper a “converse” theorem is established on the set of achievable quintuples (R 1 , R 2 , D 0 , D 1 , D 2 ). For the special case R 1 = R 2 = 1/2, D 0 = 0, and D 1 = D 2 = D, our result implies that D ≥ 1/5.