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.

翻译：我们研究了在有限时间范围$T$内，通过未知擦除概率的二进制擦除信道实现可靠数据传输的问题。考虑一个反馈模型，其中发射器可以偶尔向接收器查询并获取后者经历的经验擦除率。我们旨在最小化遗憾量，即在相同的块错误率下，策略相较于知道擦除概率的预言机性能的差距。在此场景中出现了学习与利用的困境——具体而言，我们需要平衡以下两方面：(i) 以合理精度学习擦除概率，以及(ii) 利用信道传输尽可能多的信息比特。我们提出两种策略：(i) 一种两阶段方法，先进行速率估计再进行传输，仅需一次查询即可实现$O({T}^{\frac23})$的遗憾；(ii) 一种采用几何递增窗口大小的窗口化策略，使用$O(\log(T))$次查询即可实现$O({\sqrt{T}})$的遗憾。