Breadth-first maximum likelihood sequence detection: basics

The problem of performing breadth-first maximum likelihood sequence detection (MLSD) under given structural and complexity constraints is solved and results in a family of optimal detectors. Given a trellis with S states, these are partitioned into C classes where B paths into each class are selected recursively in each symbol interval. The derived result is to retain only those paths which are closest to the received signal in the Euclidean (Hamming) distance sense. Each member in the SA(B, C) family of sequence detectors (SA denotes search algorithm) performs complexity constrained MLSD for the additive white Gaussian noise (AWGN) (BSC) channel. The unconstrained solution is the Viterbi algorithm (VA). Analysis tools are developed for each member of the SA(B, C) class and the asymptotic (SNR) probability of losing the correct path is associated with a new Euclidean distance measure for the AWGN case, the vector Euclidean distance (VED). The traditional Euclidean distance is a scalar special case of this, termed the scalar Euclidean distance (SED). The generality of this VED is pointed out. Some general complexity reductions exemplify those associated with the VA approach.