The Gilbert-Elliott channel: equivalent models and bounds on the capacity

Different models are in use for describing the statistical structure of the error process in digital transmission systems. The models proposed by Gilbert/Elliott and McCullough are described as special cases of a more general hidden Markov model. For this structure a necessary and sufficient criterion for the equivalence of two models is given. It is proved that, under certain conditions, Gilbert-Elliott and McCullough models are equivalent. Because no explicit expression for the capacity of these channels is known, bounds are used for approximation. These bounds are in general not identical for equivalent models, and this fact can be utilized for optimization. It is derived that, under certain conditions, one specific model structure is optimal for the bounds on the channel capacity