We provide a mathematical framework to analyze the limits of Hybrid Automatic Repeat reQuest (HARQ) and derive analytical expressions for the most powerful test for estimating the decodability under maximum-likelihood decoding and $t$-error decoding. Furthermore, we numerically approximate the most powerful test for sum-product decoding. We compare the performance of previously studied HARQ prediction schemes and show that none of the state-of-the-art HARQ prediction is most powerful to estimate the decodability of a partially received signal vector under maximum-likelihood decoding and sum-product decoding. Furthermore, we demonstrate that decoding in general is suboptimal for predicting the decodability.

翻译：我们提出了一个数学框架来分析混合自动重传请求（HARQ）的极限，并推导出在最大似然解码和$t$错误解码条件下估计可解码性的最大功效检验的解析表达式。此外，我们数值近似了和积解码的最大功效检验。我们比较了此前研究的HARQ预测方案的性能，并表明现有的HARQ预测方法均非最大功效检验，无法在最大似然解码和和积解码条件下准确估计部分接收信号向量的可解码性。进一步地，我们证明了一般情况下解码操作对于可解码性预测是次优的。