  To ensure reliable communication in randomly varying and error-prone
channels, wireless systems use adaptive modulation and coding (AMC) as well as
hybrid ARQ (HARQ). In order to elucidate their compatibility and interaction,
we compare the throughput provided by AMC, HARQ, and their combination
(AMC-HARQ) under two operational conditions: in slow- and fast block-fading
channels. Considering both, incremental redundancy HARQ (HARQ-IR) and
repetition redundancy HARQ (HARQ-RR) we optimize the rate-decision regions for
AMC/HARQ and compare them in terms of attainable throughput. Under a fairly
general model of the channel variation and the decoding functions, we conclude
that i) adding HARQ on top of AMC may be counterproductive in the high average
signal- to-noise ratio regime for fast fading channels, and ii) HARQ is useful
for slow fading channels, but it provides moderate throughput gains. We provide
explanations for these results which allow us to propose paths to improve
AMC-HARQ systems.
