Source Coding for Multiple Descriptions II: A Binary Source
Hans S. Witsenhausen, Aaron D. Wyner · Bell System Technical Journal · 1981
A uniformly distributed (iid) binary source is encoded into two binary data streams at rates R1and R2, 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 D1, D2, respectively), and by observing both sequences, a decoder can obtain a better approximation of the source (at average error rate D0). In this paper a “converse” theorem is established on the set of achievable quintuples (R1, R2, D0, D1, D2). For the special case R1= R2= 1/2, D0= 0, and D1= D2= D, our result implies that D ≥ 1/5.