Communication issues are described in terms of macro operations between the data and the observation spaces. The problem of recovering the data is related to the inversion of an operator (the channel mapping); for this reason results available in linear algebra and functional analysis are applicable. Traditional concepts in communications are identified with these operations. An approach to the maximum-likelihood sequence estimator based on a sufficient statistic derived from these concepts is proposed. Intersymbol interference is removed by linear equalization, and a Viterbi-like dynamic programming algorithm takes into account the correlated noise in the metric evaluation. The performance of suboptimal receivers obtained by means of metric simplification is analyzed.>

The Viterbi algorithm is an efficient technique to estimate the state sequence of a discrete-time finite-state Markov process in the presence of memoryless noise. This work sets up a relationship to a general class of linear and nonlinear fast algorithms such as FFT, FWT, and optimal sorting. The performance of a Viterbi detector is a function of the minimum distance between signals in the observation space of the estimated Markov process. It is shown that this distance may efficiently be calculated with dynamic programming using a slightly modified Viterbi algorithm of an increased basis.