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On Properties of Locally Optimal Multiple Description Scalar Quantizers With Convex Cells | IEEE Journals & Magazine | IEEE Xplore

On Properties of Locally Optimal Multiple Description Scalar Quantizers With Convex Cells


Abstract:

It is known that the generalized Lloyd method is applicable to locally optimal multiple description scalar quantizer (MDSQ) design. However, it remains unsettled when the...Show More

Abstract:

It is known that the generalized Lloyd method is applicable to locally optimal multiple description scalar quantizer (MDSQ) design. However, it remains unsettled when the resulting MDSQ is also globally optimal. We partially answer the above question by proving that for a fixed index assignment there is a unique locally optimal fixed-rate MDSQ of convex cells under Trushkin's sufficient conditions for the uniqueness of locally optimal fixed-rate single description scalar quantizer. This result holds for fixed-rate multiresolution scalar quantizer (MRSQ) of convex cells as well. Thus, the well-known log-concave probability density function (pdf) condition can be extended to the multiple description and multiresolution cases.
Published in: IEEE Transactions on Information Theory ( Volume: 55, Issue: 12, December 2009)
Page(s): 5591 - 5606
Date of Publication: 17 November 2009

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