In this paper, a mathematical framework for APP decoding of binary linear block codes on the Gilbert-Elliott channel (GEC) is developed. For this purpose, the theory of group representations and finite state machines are combined for deriving a `dual APP' algorithm for the GEC. The presented approach belongs to the class of single-sweep algorithms. As such, complexity benefits of the dual approaches are preserved while additional storage savings are obtained over other single sweep algorithms. The presented APP decoding technique also takes account of the increasing demand for efficient utilization of bandwidth making higher rate codes more desirable.
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