On Reliability Function of Gaussian Channel with Noisy Feedback: Zero Transmission Rate

TL;DR

This paper analyzes the reliability function of a Gaussian communication channel with noisy feedback, demonstrating that even with feedback noise, the error exponent improves over no-feedback scenarios, especially with small feedback noise.

Contribution

The paper extends previous methods to Gaussian channels with noisy feedback, showing improved error exponents and quantifying gains for small feedback noise levels.

Findings

Achievable error exponent exceeds no-feedback channel for any finite feedback noise.

Method improves error exponents over earlier BSC-based methods.

Small feedback noise yields up to 23.6% gain in error exponent.

Abstract

For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also feedback channel with independent additive Gaussian noise, and the transmitter observes without delay all outputs of the forward channel via that feedback channel. Transmission of nonexponential number of messages is considered and the achievable decoding error exponent for such a combination of channels is investigated. It is shown that for any finite noise in the feedback channel the achievable error exponent is better than similar error exponent of the no-feedback channel. Method of transmission/decoding used in the paper strengthens the earlier method used by authors for BSC. In particular, for small feedback noise, it allows to get the gain of 23.6% (instead of 14.3% earlier for BSC).