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Peer Evaluation : Multiple Description Vector Quantization with Lattice Codebooks: Design and Analysis
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    Multiple Description Vector Quantization with Lattice Codebooks: Design and Analysis

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    The problem of designing a multiple description vector quantizer with lattice codebook Lambda is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices A2 and Z i, i=1,2,4,8, that make use of this labeling algorithm. The high-rate squared-error distortions for this family of L-dimensional vector quantizers are then analyzed for a memoryless source with probability density function p and differential entropy h(p) < infty. For any a in (0,1) and rate pair (R,R), it is shown that the two-channel distortion d0 and the channel 1 (or channel 2) distortions ds satisfy limR infty d0 2 (2R(1+a)) = (1/4) G(Lambda) 2 2h(p) and limR infty ds 2 (2R(1-a)) = G(SL) 2 2h(p), where G(Lambda) is the normalized second moment of a Voronoi cell of the lattice Lambda and G(SL) is the normalized second moment of a sphere in L dimensions.

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    Description

    Notice (8): Undefined index: Affiliation [APP/views/pdflibraries/read.ctp, line 562]
    Title : Multiple Description Vector Quantization with Lattice Codebooks: Design and Analysis
    Author(s) : Vinay A Vaishampayan, N J A Sloane, Sergio D Servetto
    Abstract : The problem of designing a multiple description vector quantizer with lattice codebook Lambda is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices A2 and Z i, i=1,2,4,8, that make use of this labeling algorithm. The high-rate squared-error distortions for this family of L-dimensional vector quantizers are then analyzed for a memoryless source with probability density function p and differential entropy h(p) < infty. For any a in (0,1) and rate pair (R,R), it is shown that the two-channel distortion d0 and the channel 1 (or channel 2) distortions ds satisfy limR infty d0 2 (2R(1+a)) = (1/4) G(Lambda) 2 2h(p) and limR infty ds 2 (2R(1-a)) = G(SL) 2 2h(p), where G(Lambda) is the normalized second moment of a Voronoi cell of the lattice Lambda and G(SL) is the normalized second moment of a sphere in L dimensions.
    Subject : unspecified
    Area : Other
    Language : English
    Year : 2002

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    Journal : IEEE Transactions on Information Theory
    Volume : 47
    Issue : 5
    Pages : 46
    Url : http://arxiv.org/abs/math/0207289

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