Zero-rate feedback can achieve the empirical capacity

TL;DR

This paper demonstrates that zero-rate feedback can be used to asymptotically achieve the empirical capacity of a channel with an individual sequence of DMCs, enhancing communication reliability.

Contribution

It introduces a fixed input distribution strategy that asymptotically attains rates close to the mutual information, achieving empirical capacity with zero-rate feedback.

Findings

Zero-rate feedback can asymptotically achieve the empirical capacity.

The proposed strategy attains rates close to mutual information induced by the input distribution.

When the capacity-achieving input is consistent across states, the method reaches the capacity of the state-averaged channel.

Abstract

The utility of limited feedback for coding over an individual sequence of DMCs is investigated. This study complements recent results showing how limited or noisy feedback can boost the reliability of communication. A strategy with fixed input distribution $P$ is given that asymptotically achieves rates arbitrarily close to the mutual information induced by $P$ and the state-averaged channel. When the capacity achieving input distribution is the same over all channel states, this achieves rates at least as large as the capacity of the state averaged channel, sometimes called the empirical capacity.