A class of F-ary convolutional codes for finite state ISI channels

This paper presents F-ary convolutional codes for optimal decoding of pulse-amplitude-modulated (PAM) sequences over noisy finite intersymbol interference (ISI) channels. We refer to this new class of codes as `optimal convolutional codes´ (OCCs) for a channel in the sense of maximizing the minimum Euclidean Distance (ED), d<sub>min</sub>, between channel output sequences corresponding to distinct input message sequences at the Viterbi detector, super-trellis of convolutional encoder and channel. Due to the mismatch between the base fields of the convolutional encoder and channel, without resorting to analytical methods, an exhaustive computer search algorithm is proposed on a set of convolutional encoders, called `standard trellis´, which have a specific structure in common. This trellis structure offers good properties in finding d_min of a code associated with a given encoder. This search scheme, as an example, is applied to the 1+4D+D² channel, and search results have shown that the coding gains achieved are comparable to those of the best convolutional codes in a perfect response channel. To overcome the high computational complexity of optimal MLSE decoding, a new simple and efficient reduced state suboptimal decoding algorithm is also suggested