channel is a varying binary symmetric 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. 'Strictly speaking, at any rate below _C [2, pp. 180z181]. The Gilbert-Elliott channel is indecomposable and therefore _C = C = C [2, p. 1091.

For any real number θ let where [x] denotes the greatest integer not exceeding x. A method is given for computing fθ from its first few terms. A similar method is given for computing the characteristic function gθ(n) of [nθ]. The given methods converge rapidly, and generalize previous results of Bernoulli, Markorf, and Stolarsky. Note that either of the sequences fθ and gθ determines the sequence [nθ] (n = 1, 2,…).