On Reliability Function of BSC with Noisy Feedback

TL;DR

This paper investigates the reliability function of a binary symmetric channel with noisy feedback, showing that under certain conditions, feedback improves the error exponent compared to no-feedback scenarios.

Contribution

It introduces the achievable decoding error exponent for BSC with noisy feedback and identifies conditions where feedback enhances reliability.

Findings

Feedback with low crossover probability improves error exponent.

Achievable error exponent exceeds that of no-feedback channels under certain noise levels.

Provides theoretical bounds for reliability with noisy feedback.

Abstract

For 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 an exponential number of messages (i.e. the transmission rate is positive) 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 decoding error exponent of the channel without feedback.