Learning to Transmit Over Unknown Erasure Channels with Empirical Erasure Rate Feedback

TL;DR

This paper develops strategies for reliable data transmission over unknown erasure channels using limited feedback, balancing learning the channel and transmitting data to minimize regret.

Contribution

It introduces two novel algorithms that adaptively learn erasure rates with minimal feedback, achieving sublinear regret bounds in finite time.

Findings

Two-phase strategy achieves $O(T^{2/3})$ regret with one query.

Windowing strategy achieves $O( oot T)$ regret with $O(\log T)$ queries.

Proposes practical methods for adaptive transmission over unknown channels.

Abstract

We address the problem of reliable data transmission within a finite time horizon $T$ over a binary erasure channel with unknown erasure probability. We consider a feedback model wherein the transmitter can query the receiver infrequently and obtain the empirical erasure rate experienced by the latter. We aim to minimize a regret quantity, i.e. how much worse a strategy performs compared to an oracle who knows the probability of erasure, while operating at the same block error rate. A learning vs. exploitation dilemma manifests in this scenario -- specifically, we need to balance between (i) learning the erasure probability with reasonable accuracy and (ii) utilizing the channel to transmit as many information bits as possible. We propose two strategies: (i) a two-phase approach using rate estimation followed by transmission that achieves an $O({T}^{\frac 23})$ regret using only one query, and (ii) a windowing strategy using geometrically-increasing window sizes that achieves an $O({\sqrt{T}})$ regret using $O(\log(T))$ queries.