Capacity and Coding for the G

Ahstrrrrt -The Gilbert-Elliott channel is a varying binary symmetr ic channel with crossover probabilities determined by a binary-state Markov process. In general, such a channel has a memory that depends on the transition probabilities between the states. First, a method of calculating the capacity of this channel is introduced and applied to several examples: then the question of coding is addressed. In the conventional usage of varying channels, a code suitable for memoryless channels is used in conjunction with an interleaver, with the decoder considering the deinterleaved symbol stream as the output of a derived memoryless channel. The transmission rate in such uses is limited by the capacity of this memoryless channel, which is, however, often considerably less than the capacity of the original channel. In this work a decision-feedback decoding algorithm, that completely recovers this capacity loss, is introduced. It is shown that the performance of a system incorporating such an algorithm is determined by an equivalent genie-aided channel, the capacity of which equals that of the original channel. Also, the calculated random coding exponent of the genie-aided channel indicates a considerable increase in the cutoff rate over the conventionally derived memoryless channel.