  Fog radio access network (Fog-RAN), which pushes the caching and computing
capabilities to the network edge, is capable of efficiently delivering contents
to users by using carefully designed caching placement and content replacement
algorithms. In this paper, the transmission scheme design and coding parameter
optimization will be considered for coded caching in Fog-RAN, where the
reliability of content delivery, i.e., content outage probability, is used as
the performance metric. The problem will be formulated as a complicated
multi-objective probabilistic combinatorial optimization. A novel maximum
b-matching approach will then be proposed to obtain the Pareto optimal solution
with fairness constraint. Based on the fast message passing approach, a
distributed algorithm with a low memory usage of O(M + N) is also proposed,
where M is the number of users and N is the number of Fog-APs. Although it is
usually very difficult to derive the closed-form formulas for the optimal
solution, the approximation formulas of the content outage probability will
also be obtained as a function of coding parameters. The asymptotic optimal
coding parameters can then be obtained by defining and deriving the outage
exponent region (OER) and diversity-multiplexing region (DMR). Simulation
results will illustrate the accuracy of the theoretical derivations, and verify
the outage performance of the proposed approach. Therefore, this paper not only
proposes a practical distributed Fog-AP selection algorithm for coded caching,
but also provides a systematic way to evaluate and optimize the performance of
Fog-RANs.
