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

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. 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 et al. can be achieved. Furthermore, for three descriptions and finite lattice vector dimensions, we show that the IA-based approach yields a smaller rate loss than the recently proposed source-splitting approach. Index Terms distributed source coding, high-rate quantization, lattice quantization, multiple description coding, random binning, vector quantization. This research was performed while all authors were at Delft University of Technology, Delft, The Netherlands, and was supported by the Technology Foundation STW, applied science division of NWO and the technology programme of the ministry of Economics Affairs. Jan Østergaard ([email protected]) is now with Aalborg University, Aalborg, Denmark. Richard Heusdens ([email protected]) is with Delft University of Technology, Delft, The Netherlands, and Jesper Jensen ([email protected]) is now with Oticon, Copenhagen, Denmark. This work was presented in part at the International Symposium on Information Theory, 2005 and 2006.