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

机译：具有凸单元的局部最优多描述标量量化器的性质

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摘要

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.
机译：众所周知，广义的Lloyd方法适用于局部最优的多描述标量量化器（MDSQ）设计。但是，当生成的MDSQ也是全局最优时，它仍未解决。我们通过证明对于固定索引分配，在Trushkin的局部最优固定速率单描述标量量化器的唯一性的充分条件下，存在凸单元的唯一局部最优固定速率MDSQ，从而部分回答了上述问题。该结果也适用于凸单元的固定速率多分辨率标量量化器（MRSQ）。因此，众所周知的对数凹凹概率密度函数（pdf）条件可以扩展到多种描述和多分辨率情况。

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