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On the Design of Optimal Noisy Channel Scalar Quantizer with Random Index Assignment | IEEE Journals & Magazine | IEEE Xplore

On the Design of Optimal Noisy Channel Scalar Quantizer with Random Index Assignment


Abstract:

The general approach in a noisy channel scalar quantizer design is an iterative descent algorithm, which guarantees only a locally optimal solution. While sufficient cond...Show More

Abstract:

The general approach in a noisy channel scalar quantizer design is an iterative descent algorithm, which guarantees only a locally optimal solution. While sufficient conditions under which the local optimum becomes a global optimum are known in the noiseless channel case, such sufficient conditions were not derived for the noisy counterpart. Moreover, efficient globally optimal design techniques for general discrete distributions in the noiseless case exist; however, they seem not to extend to the noisy scenario when a fixed index assignment is assumed. Recently, the design of noisy channel scalar quantizer with random index assignment (RIA) was proposed using a locally optimal iterative algorithm. In this paper, we derive sufficient conditions for the uniqueness of a local optimum, which, thus, guarantee the global optimality of the solution. These sufficient conditions are satisfied for a log-concave probability density function which is, additionally, symmetric around its mean. Furthermore, we show that, assuming an RIA, the globally optimal design for general discrete sources can also be carried out efficiently.
Published in: IEEE Transactions on Information Theory ( Volume: 62, Issue: 2, February 2016)
Page(s): 724 - 735
Date of Publication: 22 December 2015

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