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

## TL;DR

This paper calculates the capacity of the Gilbert–Elliott channel when the state sequence is revealed to the encoder and needs to be nearly losslessly transmitted to the receiver.

## Contribution

The paper shows that the channel capacity is independent of the timing of state information availability at the encoder.

## Key findings

- The capacity of the Gilbert–Elliott channel is determined for a specific transmission setting.
- A Block-Markov coding scheme with backward decoding achieves the calculated capacity.
- The capacity remains the same regardless of the state information timing at the encoder.

## Abstract

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.