Optimal Two-Description Scalar Quantizer Design

Abstract

Multiple description quantization is a signal compression technique for robust networked multimedia communication. In this paper we consider the problem of optimally quantizing a random variable into two descriptions, with each description being produced by a side quantizer of convex codecells. The optimization objective is to minimize the expected distortion given the probabilities of receiving either and both descriptions. The problem is formulated as one of shortest path in a weighted directed acyclic graph with constraints on the number and types of edges. An $O(K_1K_2N^3)$ time algorithm for designing the optimal two-description quantizer is presented, where $N$ is the cardinality of the source alphabet, and $K_1$, $K_2$ are the number of codewords of the two quantizers, respectively. This complexity is reduced to $O(K_1K_2N^2)$ by exploiting the Monge property of the objective function. Furthermore, if $K_1 = K_2 = K$ and the two descriptions are transmitted through two channels of the same statistics, then the optimal two-description quantizer design problem can be solved in $O(KN^2)$ time.