# New applications and properties of the symmetric cutoff rate of discrete-time channels with intersymbol interference

## Abstract

Summary form only given, as follows. Several new applications and properties of the symmetric cutoff rate, which have not been exploited previously, are presented. The channel model is the discrete-time channel with intersymbol interference (ISI), where the independent inputs are binary and of equal probability. The unit-sample response of the transversal filter model of the channel is a finite-length sequence of unit energy. The noise added to the filter output is white Gaussian with mean zero and variance N0/2, where N0 is the one-sided noise power spectral density. The symmetric cutoff rate, which is defined for unquantized maximum-likelihood sequence decoding (MLSD), is first derived for this channel model. Using random-coding arguments, a simple expression is then developed to obtain a computationally efficient, tight approximation of the minimum squared Euclidean distance, which determines performance bounds for uncoded binary signaling over ISI channels using MLSD. This novel approach does not require identification of a specific error sequence which produces that minimum distance. Next, a method to approximate the unit-sample response of so-called minimum distance channels (MDCs) is described.