The design of finite-length decision-feedback equalization (DFE) forward and feedback filters under the assumption of genie-aided feedback and independent and equally likely transmitted symbols is considered. It is shown that the problem of determining DFE filters that minimize the probability of symbol error at high signal-to-noise ratio (SNR) is equivalent to finding the hyperplane that maximally separates two given finite groups of points in a finite-dimensional Euclidean space. The latter task can be formulated as a quadratic program which is readily solved numerically. It is also shown that the problem of finding finite-length DFE filters that minimize the probability of symbol error at any SNR subject to a certain separation condition is a convex optimization problem. The case where the transmitted data is coded using a runlength-limited code is also investigated. Examples show that this criterion yields a performance that is better than zero-forcing DFE on severely distorted channels at high SNR.

Two algorithms for characterization of input error events producing specified distance at the output of certain binary-input partial-response (PR) channels are presented. Lists of error events are tabulated for PR channels of interest in digital recording.

The exact computation of the symbol error probability of systems using decision feedback equalization is difficult due to the propagation of errors. New upper bounds to the error probability of decision feedback equalization, which take error propagation into account, are developed. The derivations of the bounds assume a causal channel response, independent data symbols, and independent noise samples. The bounds are valid for any noise process that has a symmetric and unimodal probability density function. In some cases, the new bounds are significantly tighter than a well-known upper bound of D.L. Duttweiler et al. (1974).>

A new upper bound on the probability of error for decision feedback equalizers that is valid for serially independent and dependent stationary noise processes was presented by P. Kabaila (1987). It is shown that a bound of D.L. Duttweiler et al. (1974) is tighter than the bound of Kabaila when the noise component shows no serial dependence and with equalization over the full channel response length.>