Fundamental Limits of Cache-Aided Interference Management
  We consider a system comprising a library of $N$ files (e.g., movies) and a wireless network with $K_T$ transmitters, each equipped with a local cache of size of $M_T$ files, and $K_R$ receivers, each equipped with a local cache of size of $M_R$ files. Each receiver will ask for one of the $N$ files in the library, which needs to be delivered. The objective is to design the cache placement (without prior knowledge of receivers' future requests) and the communication scheme to maximize the throughput of the delivery. In this setting, we show that the sum degrees-of-freedom (sum-DoF) of $\min\left\{\frac{K_T M_T+K_R M_R}{N},K_R\right\}$ is achievable, and this is within a factor of 2 of the optimum, under one-shot linear schemes. This result shows that (i) the one-shot sum-DoF scales linearly with the aggregate cache size in the network (i.e., the cumulative memory available at all nodes), (ii) the transmitters' and receivers' caches contribute equally in the one-shot sum-DoF, and (iii) caching can offer a throughput gain that scales linearly with the size of the network.   To prove the result, we propose an achievable scheme that exploits the redundancy of the content at transmitters' caches to cooperatively zero-force some outgoing interference and availability of the unintended content at receivers' caches to cancel (subtract) some of the incoming interference. We develop a particular pattern for cache placement that maximizes the overall gains of cache-aided transmit and receive interference cancellations. For the converse, we present an integer optimization problem which minimizes the number of communication blocks needed to deliver any set of requested files to the receivers. We then provide a lower bound on the value of this optimization problem, hence leading to an upper bound on the linear one-shot sum-DoF of the network, which is within a factor of 2 of the achievable sum-DoF. 
Navid Naderializadeh, Mohammad Ali Maddah-Ali, and A. Salman   Avestimehr
cs.IT math.IT