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Multiple-description vector quantization with lattice codebooks: design and analysis

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3 Author(s)
Vaishampayan, V.A. ; AT&T Shannon Lab., Florham Park,NJ, USA ; Sloane, N. ; Servetto, S.D.

The problem of designing a multiple-description vector quantizer with lattice codebook Λ 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 Zi, 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 (PDF) p and differential entropy h(p)<∞. For any a ε (0, 1) and rate pair (R, R), it is shown that the two-channel distortion d¯o and the channel 1 (or channel 2) distortion d¯s satisfy limR→∞o22R(1+a) =¼G(Λ)22h(p) and limR→∞ s22R(1-a)=G(SL)22h(p) where G(Λ) is the normalized second moment of a Voronoi cell of the lattice Λ and G(SL) is the normalized second moment of a sphere in L dimensions

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Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 5 )