Optimal Quantizer Design for Noisy Channels: An Approach to Combined Source-Channel Coding.
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In this paper, we present an analysis of the zero-memory quantization of memoryless sources when the quantizer output is to be encoded and transmitted across a noisy channel. Necessary conditions for the joint optimization of the quantizer and the encoder/decoder pair are presented and a recursive algorithm for obtaining a locally optimum system is developed. The performance of this locally optimal system, obtained for the class of generalized Gaussian distributions and the Binary Symmetric Channel is compared against the Optimum Performance Theoretically Attainable (using Rate-Distortion theoretic arguments), as well as against the performance of Loyd-Max quantizers encoded using Natural Binary Codes. It is shown that this optimal design could result in substantial performance improvements. The performance improvements are more noticeable at high bit rates and for more broad-tailed densities.