  In a Fog Radio Access Network (Fog-RAN), edge caching is combined with
cloud-aided transmission in order to compensate for the limited hit probability
of the caches at the base stations (BSs). Unlike the typical wired scenarios
studied in the networking literature in which entire files are typically
cached, recent research has suggested that fractional caching at the BSs of a
wireless system can be beneficial. This paper investigates the benefits of
fractional caching in a scenario with a cloud processor connected via a
wireless fronthaul link to a BS, which serves a number of mobile users on a
wireless downlink channel using orthogonal spectral resources. The fronthaul
and downlink channels occupy orthogonal frequency bands. The end-to-end
delivery latency for given requests of the users depends on the HARQ processes
run on the two links to counteract fading-induced outages. An analytical
framework based on theory of Markov chains with rewards is provided that
enables the optimization of fractional edge caching at the BSs. Numerical
results demonstrate meaningful advantages for fractional caching due to the
interplay between caching and HARQ transmission. The gains are observed in the
typical case in which the performance is limited by the wireless downlink
channel and the file popularity distribution is not too skewed.
