Index mapping for bit-error resilient multiple description lattice vector quantizer
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Multiple Description Coding (MDC) is a source coding technique which generates several descriptions of a signal such that the reconstruction gradually refines with the number of decoded descriptions. Conventionally, the design of MDC has largely focused on combating the description loss. This thesis considers the construction of robust multiple description lattice vector quantizers (MDLVQ) by addressing the problem of designing an index mapping able to combat bit errors.
We consider the scenario when the first description is received correctly at the decoder while the second one may carry bit errors. Our approach is to use a good assignment of the central lattice points to pairs of side lattice points, as developed in previous work, and design the mapping of the second description side lattice points to binary indexes such that the expected channel distortion to be minimized. In this thesis, we propose two methods to tackle this problem.
The first method is a binary switching heuristic algorithm, which starts with an initial mapping and iteratively switches two indexes such that the distortion is decreased. This algorithm only guarantees a locally optimal solution whose quality depends on the initial configuration.
The second approach attempts to increase the minimum Hamming distance between possible indexes in the second description when the first description is fixed. This is achieved using a structured construction as follows. First the set of second description side lattice points is partitioned into Voronoi regions of a carefully chosen coarse lattice. Next a channel code with high Hamming distance is picked, 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. We point out that in order to achieve good performance the mapping of Voronoi regions to cosets of the channel code must assign cosets close in Hamming distance to neighboring Voronoi regions. Two methods to achieve this goal are proposed and bounds on their performance are derived.
Finally, simulations are carried out to assess the practical performance of the proposed designs. Our results show significant performance improvement when the proposed index mappings are used versus non-optimized mappings.
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