  This paper studies the tradeoff between channel coding and ARQ (automatic
repeat request) in Rayleigh block-fading channels. A heavily coded system
corresponds to a low transmission rate with few ARQ re-transmissions, whereas
lighter coding corresponds to a higher transmitted rate but more
re-transmissions. The optimum error probability, where optimum refers to the
maximization of the average successful throughput, is derived and is shown to
be a decreasing function of the average signal-to-noise ratio and of the
channel diversity order. A general conclusion of the work is that the optimum
error probability is quite large (e.g., 10% or larger) for reasonable channel
parameters, and that operating at a very small error probability can lead to a
significantly reduced throughput. This conclusion holds even when a number of
practical ARQ considerations, such as delay constraints and acknowledgement
feedback errors, are taken into account.
