Rate and Nearly-Lossless State over the Gilbert–Elliott Channel

The capacity of the Gilbert-Elliott channel is calculated for a setting in which the state sequence is revealed to the encoder and is, along with the transmitted message, to be conveyed to the receiver with a vanishing symbol error rate. Said capacity does not depend on whether the state sequence is provided to the encoder strictly causally, causally, or noncausally. It can be achieved using a Block-Markov coding scheme with backward decoding.