The Theory and Applications of Multiple Description Coding

Loss of descriptions of stochastic processes transmitted over unreliable channels is typical in communication network. An intuitive approach to address this problem is to send more than one descriptions of the same sources and hope that at least one description can survive. Each description is supposed to be good enough to meet some decoder requirement if it get through itself. So these descriptions carry a lot of similar information and are dependent. However, if all these descriptions are received, we also hope the combined results to be as good as possible. This requires that the descriptions are far apart and thus can not be individually good. The multiple description problem refers to ”if an information source is described by two or more separate descriptions, what are the concurrent limitations on qualities of these descriptions taken separately and jointly?”[1]. In other words, the fundamental problem is how can we achieve tradeoff between making descriptions individually good and sufficiently different. A multiple description coding(MDC) model with two channels and three receivers is shown in figure 1. An encoder is given a symbol sequence yielded by a stochastic process {Xk}, where Xk’s are independent identically distributed (i.i.d.) according to some known distribution p(x). Two descriptions of the same sequence, of rate R1 and R2, are sent to decoder 1 and 2 through two channels, respectively. The central decoder 0 receives information over both two channels while the other two only receive information over their respective channels. All decoders have their own specific quality requirement in terms of distortion, denoted by D0, D1 and D2. One key theoretical problem in MDC was answered by El Gamal and T. Cover in [2]. Their proof gave a general bound, in usual Shannon sense ,for the achievable set of values of the quintuple (R1, R2,D0,D1,D2), thus determine what are the achievable rates R1 and R2 given distortions D0, D1 and D2. Ozarow further showed a tight bound for memoryless Gaussian source with with mean-square error(MSE). Unfortunately, these bound can only be achieved by coding arbitrarily long sequences, which are not applicable in real network.