Capacity and coding for the gilbert-elliott channels

Abstract

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.

Dispersion of the Gilbert-Elliott channel

“…As shown in [5], when the state transition probability decreases to 0 the capacity increases to . This is sometimes interpreted as implying that if the state is unknown at the receiver slower dynamics are advantageous.…”

On Decoding Binary Quasi-Perfect Codes Over Markov Noise Channels

“…and the resulting channel reduces to the (memoryless) binary symmetric channel with crossover probability or CBER p (which we denote by BSC(p)). Note that this (memory-one) Markov noise channel is a special case of the Gilbert-Elliott channel [6] (realized when the probability for causing an error equals zero in the "good state" and one in the "bad state").…”

“…Progress has been achieved on the statistical and information theoretic modeling of channels with memory (e.g., see [1], [6], [10], [11]), as well as on the design of effective iterative decoders for such channels (e.g., see [2], [3], [7], [8]). However, little is known about the structure of optimal maximum likelihood (ML) decoders for such channels.…”

Hidden Markov Model for distributed video coding

“…The GE channel was investigated by Garcia-Frias [7] as a model for the correlation between X and Y , we use it as a model for the source. The estimation of the GE channel parameters was carried out by [8]. We propose the joint estimation of the model parameters This research was partially supported by the French European Commission in the framework of the FP7 Network of Excellence in Wireless COMmunications NEWCOM++ (contract n.216715).…”