Gaussian broadcast channels with receiver cache assignment

This paper considers a K-user Gaussian broadcast channel (BC) where receivers are equipped with cache memories. Lower and upper bounds are established on the capacity-memory tradeoff, i.e., the largest rate achievable for given cache-memories. The lower bound is based on a joint cache-channel coding scheme which generalizes the recently proposed piggyback coding to Gaussian BCs with unequal cache sizes. This paper also establishes lower and upper bounds on the global capacity-memory tradeoff, i.e., the maximum capacity-memory tradeoff over all possible cache assignments subject to a total cache memory constraint. The bounds match when the total cache memory is sufficiently large. It is shown that significantly larger rates can be achieved by carefully assigning larger cache memories to weaker receivers. In particular, cache allocation allows communication at rates that are (fundamentally) impossible to achieve with equal cache assignment. This shows the merit in carefully designing the cache size allocation in conjunction with channel qualities.