Source Coding for Multiple Descriptions
Jack K. Wolf, Aaron D. Wyner, J. Ziv · Bell System Technical Journal · 1980
This paper discusses an idealization of the situation in which it is required to send information over two separate channels, as in a packet communication network, and it is desired to recover as much as possible of the original information should one of the channels break down. Let {Xk}∞k–1be a sequence of independent copies of the binary random variable X, where Pr[X = 0} = Pr{X = 1} = 1/2. Assume that this sequence appears at a rate of one symbol per second as the output of a data source. An encoder observes this sequence and emits two binary sequences at rates R1, R2≤ 1. These sequences are such that, by observing either one, a decoder can recover a good approximation to the source output and, by observing both sequences, a decoder can obtain a better approximation to the source output Letting D1, D2, D0be the error rates that result when the streams at rate R1, rate R2, and both streams are used by a decoder, respectively, our problem is to determine (in the usual Shannon sense) the set of achievable quintuples (R1, R2, D1, D1, D2). Our main result is a “converse” theorem that gives a necessary condition on the achievable quintuples.