Multiple Description Lattice Vector Quantization Multiple Description Lattice Vector Quantization

This thesis studies the multiple description vector quantization with lattice codebooks (MDLVQ). The design of index assignment is crucial to the performance of MDLVQ. However, to our best knowledge, none of previous index assignment algorithms for MDLVQ is optimal. In this thesis, we propose a simple linear-time index assignment algorithm for MDLVQ with any K ≥ 2 balanced descriptions. We prove, under the assumption of high resolution, that the algorithm is optimal for K = 2. The optimality holds for many commonly used good lattices of any dimensions, over the entire range of achievable central distortions given the side entropy rate. The optimality is in terms of minimizing the expected distortion given the side description loss rate and given the side entropy rate. We conjecture it to be optimal for K > 2 in general. We also made progress in the analysis of MDLVQ performance. The first exact closed form expression of the expected distortion was derived for K = 2. For K > 2, we improved the current asymptotic expression of the expected distortion.