Redundancy in quantisers for noisy channels

This paper presents a study of the nature of optimal quantiser/dequantiser pairs for use with binary symmetric channels with moderate to high error rates. It is well known that some codewords of such quantisers are never output, because there is always another codeword with lower expected distortion. This paper investigates how high the bit error rate must be for this phenomenon to occur. It also investigates the nature of optimal quantisers for extremely noisy channels, in which the error probability is almost 1/2.