  We state and solve a problem of the optimal geographic caching of content in
cellular networks, where linear combinations of contents are stored in the
caches of base stations. We consider a general content popularity distribution
and a general distribution of the number of stations covering the typical
location in the network. We are looking for a policy of content caching
maximizing the probability of serving the typical content request from the
caches of covering stations. The problem has a special form of monotone
sub-modular set function maximization. Using dynamic programming, we find a
deterministic policy solving the problem. We also consider two natural greedy
caching policies. We evaluate our policies considering two popular stochastic
geometric coverage models: the Boolean one and the
Signal-to-Interference-and-Noise-Ratio one, assuming Zipf popularity
distribution. Our numerical results show that the proposed deterministic
policies are in general not worse than some randomized policy considered in the
literature and can further improve the total hit probability in the moderately
high coverage regime.
