  In response to a comment on one of our manuscript, this work studies the
posterior channel and noise distributions conditioned on the NACKs and ACKs of
all previous transmissions in HARQ system with statistical approaches. Our main
result is that, unless the coherence interval (time or frequency) is large as
in block-fading assumption, the posterior distribution of the channel and noise
either remains almost identical to the prior distribution, or it mostly follows
the same class of distribution as the prior one. In the latter case, the
difference between the posterior and prior distribution can be modeled as some
parameter mismatch, which has little impact on certain type of applications.
