On zero-rate error exponent for BSC with noisy feedback

TL;DR

This paper investigates the error exponent for zero-rate communication over a BSC with noisy feedback, showing that reliable transmission can be improved with low-noise feedback channels.

Contribution

It introduces a lower bound for the error exponent in BSC with noisy feedback and demonstrates conditions under which feedback improves error performance.

Findings

Feedback noise level affects error exponent improvement.

Lower bounds for error exponents are established.

Method can be extended to positive transmission rates.

Abstract

For the information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of the forward channel via that feedback channel. The transmission of a nonexponential number of messages (i.e. the transmission rate equals zero) is considered. The achievable decoding error exponent for such a combination of channels is investigated. It is shown that if the crossover probability of the feedback channel is less than a certain positive value, then the achievable error exponent is better than the similar error exponent of the no-feedback channel. The transmission method described and the corresponding lower bound for the error exponent can be strengthened, and also extended to the positive transmission rates.