Abstract

This paper investigates the optimal quantisation decoder to use for a range of channel conditions when the encoder is unaware of the channel error rate. Closed form expressions are derived for the case of a uniformly distributed signal and a uniform quantiser with three common codeword assignment schemes. These expressions are valid for a memoryless binary symmetric channel with an arbitrary error rate. It is shown that when natural binary coding is used, then the optimal decoder is of the same form as the decoder for a noiseless channel but scaled by a factor of 1-2epsilon. However, the results for other codeword assignments are more complicated. These results are compared with numerical results obtained for the case of a Gaussian input variable.

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