Coding for the control of intersymbol interference in baseband channels

The relationship between the structure of line codes and the error probability for baseband PCM systems with intersymbol interference is studied for a broad class of finite-state-machine codes. The model for a repeatered transmission line is reduced to a digital model including the line encoder, linear dispersive digital channel, additive Gaussian noise, and a fixed threshold detector. The error probability for a first order channel model (exponential response) is then found numerically using the Gram-Charlier series representation for the Gaussian noise probability density function. In order to accomplish this computation, the moments of the intersymbol interference are derived for this channel model via a property of the encoded channel sequence statistics. The error probability results are used to show that a simple approximation for channels which cause appreciable intersymbol interference over a span of many symbols (for example, more than fifty) provides accurate results. This approximation demonstrates the multimodal nature of the probability density of intersymbol interference, and suggests a new method of decision feedback equalization which removes most of the deleterious effects of the intersymbol interference on the error probability. It is also shown that the error propagation which is inherent in decision feedback equalizers can be effectively controlled with this new equalizer.