A unified framework for finite-memory detection

  • Authors:
  • G. Ferrari;G. Colavolpe;R. Raheli

  • Affiliations:
  • Dept. of Inf. Eng., Univ. of Parma, Italy;-;-

  • Venue:
  • IEEE Journal on Selected Areas in Communications
  • Year:
  • 2006

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Abstract

In this paper, we present a general approach to finite-memory detection. From a semi-tutorial perspective, a number of previous results are rederived and new insights are gained within a unified framework. A probabilistic derivation of the well-known Viterbi algorithm, forward-backward, and sum-product algorithms, shows that a basic metric emerges naturally under very general causality and finite-memory conditions. This result implies that detection solutions based on one algorithm can be systematically extended to other algorithms. For stochastic channels described by a suitable parametric model, a conditional Markov property is shown to imply this finite-memory condition. This conditional Markov property, although seldom met exactly in practice, is shown to represent a reasonable and useful approximation in all considered cases. We consider, as examples, linear predictive and noncoherent detection schemes. While good performance for increasing complexity can often be achieved with a finite-memory detection strategy, key issues in the design of detection algorithms are the computational efficiency and the performance for limited complexity.