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

On the Limits of HARQ Prediction for Short Deterministic Codes with Error Detection in Memoryless Channels (Extended Version with Proofs)