On Using Feedback in a Gaussian Channel

TL;DR

This paper investigates the use of feedback in a Gaussian channel with additive noise, demonstrating improved error exponents and transmission efficiency when feedback noise is small, extending previous methods to Gaussian channels.

Contribution

It introduces an enhanced transmission method leveraging feedback in Gaussian channels, achieving higher error exponents compared to earlier approaches.

Findings

Achieves a 33.3% gain in error exponent with small feedback noise.

Extends previous feedback methods from BSC to Gaussian channels.

Improves transmission reliability at zero transmission rate.

Abstract

For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also another channel with independent additive Gaussian noise (the feedback channel), and the transmitter observes without delay all outputs of the forward channel via that channel. Transmission of nonexponential number of messages is considered (i.e. transmission rate equals zero) and the achievable decoding error exponent for such a combination of channels is investigated. The transmission method strengthens the method used by authors earlier for BSC and Gaussian channels. In particular, for small feedback noise, it allows to gain 33.3\% (instead of 23.6\% earlier in the similar case of Gaussian channel).