  We address the worst-user bottleneck of wireless coded caching, which is
known to severely diminish cache-aided multicasting gains due to the
fundamental worst-channel limitation of multicasting transmission. We consider
the quasi-static Rayleigh fading Broadcast Channel, for which we first show
that the effective coded caching gain of the XOR-based standard coded-caching
scheme completely vanishes in the low-SNR regime. Then, we reveal that this
collapse is not intrinsic to coded caching. We do so by presenting a novel
scheme that can fully recover the coded caching gains by capitalizing on one
aspect that has to date remained unexploited: the shared side information
brought about by the effectively unavoidable file-size constraint. As a
consequence, the worst-user effect is dramatically ameliorated, as it is
substituted by a much more subtle worst-group-of-users effect, where the
suggested grouping is fixed, and it is decided before the channel or the
demands are known. In some cases, the theoretical gains are completely
recovered, and this is done without any user selection technique. We analyze
the achievable rate performance of the proposed scheme and derive insightful
performance approximations which prove to be very precise.
