Quantization Over Discrete Noisy Channels Using Rate-One Convolutional Codes

Abstract

We consider high-rate scalar quantization of a memoryless source for transmission over a binary symmetric channel. It is assumed that, due to its suboptimality, the quantizer's output is redundant. Our aim is to make use of this redundancy to combat channel noise. A rate-one convolutional code is introduced to convert this natural redundancy into a usable form. at the receiver, a maximum a posteriori decoder is employed. An upper bound on the average distortion of the proposed system is derived. An approximation of this bound is computable and we search for that convolutional code which minimizes the approximate upper bound. simulation results for a generalized Gaussian source with parameter a = 0.5 at rate 4 bits/sample and channel crossover provability 0.005 show improvement of 11.9 dB in signal-to-noise ratio over the Lloyd-Max quantizer and 4.6 dB over Farvardin and Vaishampayan's channel-optimized scalar quantizer.