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 repeat 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 found numerically using the Gram-Charlier series representation for the Gausian 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.