Evaluation of the exponent function E(R) for channels with intersymbol interference

The exponent function E(R), a practical measure, is used to study two kinds of decoders having 2 exp l (l = 1, 2, . . .) quantization levels in a communication channel with intersymbol interference: a decoder which takes account of channel memory, and a decoder which does not. The values of E(R) for the same kind of decoder and an increased number of quantization levels, and for the two different kinds of decoder and the same number of quantization levels, are analytically compared for a channel with intersymbol interference of length 1. It is shown that increasing the number of quantization levels for a given type of detector, or taking account of channel memory with a given number of decoder quantization levels, can decrease the upper limit of the error probability. A comparison of channel capacities is shown to yield similar conclusions.