$n$-Channel Asymmetric Entropy-Constrained Multiple-Description Lattice Vector Quantization

Abstract

This paper is about the design and analysis of an index-assignment (IA)-based multiple-description coding scheme for the n-channel asymmetric case. We use entropy constrained lattice vector quantization and restrict attention to simple reconstruction functions, which are given by the inverse IA function when all descriptions are received or otherwise by a weighted average of the received descriptions. We consider smooth sources with finite differential entropy rate and MSE fidelity criterion. As in previous designs, our construction is based on nested lattices which are combined through a single IA function. The results are exact under high-resolution conditions and asymptotically as the nesting ratios of the lattices approach infinity. For any n, the design is asymptotically optimal within the class of IA-based schemes. Moreover, in the case of two descriptions and finite lattice vector dimensions greater than one, the performance is strictly better than that of existing designs. In the case of three descriptions, we show that in the limit of large lattice vector dimensions, points on the inner bound of Pradhan can be achieved. Furthermore, for three descriptions and finite lattice vector dimensions, we show that the IA-based approach yields, in the symmetric case, a smaller rate loss than the recently proposed source-splitting approach.