Index Mapping for Bit-Error Resilient Multiple Description Lattice Vector Quantizer

In conventional multiple description coding (MDC), two descriptions of a source are generated and sent over ON/OFF channels. In this paper, we are interested in exploiting the redundancy built in MDC to additionally confer robustness against other channel errors. In particular, we consider a multiple description lattice vector quantizer (MDLVQ) whose output (a pair of side lattice points) is mapped to a pair of binary indexes and each index is sent over a binary channel. One channel is noiseless, while the other is noisy. Thus, at the decoder, one description is received error-free, while the other may carry bit errors. Then the decoder uses the error-free description as side information to improve the reconstruction. The effectiveness of the decoder in alleviating the impact of bit errors depends on the mapping $\gamma $ of side lattice points to binary indexes. We propose the design of a structured bit-error resilient mapping $\gamma $ . For this, the set of side lattice points is first partitioned using Voronoi regions of an appropriate coarse lattice. Next a good linear channel code is selected, each Voronoi region is assigned a coset of this channel code, and the side lattice points within each Voronoi region are mapped to binary sequences in the corresponding coset. In addition, we argue that the performance of $\gamma $ is improved by assigning cosets close in Hamming distance to neighboring Voronoi regions, and propose a technique to achieve this goal. We derive a lower bound on the error correction performance of the proposed mapping $\gamma $ in terms of the performance of the channel code $C$ used in its construction. Interestingly, we prove that, as the rate of the MDLVQ grows to infinity, the mapping $\gamma $ becomes as good as the code $C$ in correcting bit errors. Simulation results show the significant superiority of the proposed index mapping versus random mappings.