On trellis-based truncated-memory detection

We propose a general framework for detection over channels with infinite memory. A general truncation assumption leads automatically to the definition of a trellis diagram. A general approach to the design of forward-backward (FB) algorithms is proposed and two main classes of FB algorithms (with coupled and decoupled recursions, respectively) are presented. Moreover, it is shown that sequence detection algorithms, in the form of a Viterbi algorithm (VA), follow easily from one of the proposed classes. The generality of the proposed framework is shown by applying it to a few stochastic channels. The performance of the proposed algorithms seems to depend ultimately on the truncation length, almost irrespective of the specific detection strategy.