  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.
