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

2025-07-11

AI Summary

This paper addresses reliable transmission over a binary erasure channel (BEC) with unknown erasure probability within a finite time horizon $T$, aiming to minimize *regret*—the excess block error rate relative to an oracle strategy aware of the true erasure probability. Two adaptive transmission strategies are proposed: (1) a two-phase rate estimation scheme requiring only a single feedback instance, achieving an $O(T^{2/3})$ regret bound; and (2) an online estimation and rate-adaptive coding scheme leveraging geometrically growing sliding windows, attaining an $O(sqrt{T})$ regret upper bound. The work introduces a novel integration of non-asymptotic joint learning-and-transmission analysis, empirical erasure-rate feedback, and sliding-window estimation—enabling near-optimal throughput under infrequent feedback, closely approaching the performance achievable when channel statistics are known a priori.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Reliable data transmission over unknown erasure channels
• Minimizing regret compared to an oracle with known erasure probability
• Balancing learning erasure probability and maximizing information transmission

Innovation

• Empirical erasure rate feedback for transmission
• Two-phase approach with rate estimation
• Windowing strategy with geometric window sizes