Consider an interference channel consisting of @math transmitters and @math receivers with AWGN noise and complex channel gains, and with @math files in the system. The one-shot @math for this channel is the maximum number of receivers which can be served simultaneously with vanishing probability of error as the @math grows large, under a class of schemes known as schemes. Consider that there exists transmitter and receiver side caches which can store fractions @math and @math of the library respectively. Recent work for this cache-aided interference channel setup shows that, using a carefully designed prefetching(caching) phase, and a one-shot coded delivery scheme combined with a proper choice of beamforming coefficients at the transmitters, we can achieve a @math of @math , where @math and @math which was shown to be almost optimal. The existing scheme involves splitting the file into @math subfiles (the parameter @math is called the ), where @math can be extremely large (in fact, with constant cache fractions, it becomes exponential in @math , for large @math ). In this work, our first contribution is a scheme which achieves the same @math of @math with a smaller subpacketization than prior schemes. Our second contribution is a new coded caching scheme for the interference channel based on projective geometries over finite fields which achieves a one-shot @math of @math , with a subpacketization @math (for some prime power @math ) that is in @math , for small constant cache fraction at the receivers. To the best of our knowledge, this is the first coded caching scheme with subpacketization subexponential in the number of receivers for this setting.
We consider a cache-aided interference network which consists of a library of N files, K&#60;sub&#62;T&#60;&#x002F;sub&#62; transmitters and K&#60;sub&#62;R&#60;&#x002F;sub&#62; receivers (users), each equipped with a local cache of size M&#60;sub&#62;T&#60;&#x002F;sub&#62; and M&#60;sub&#62;R&#60;&#x002F;sub&#62; files respectively, and connected via a discrete-time additive white Gaussian noise channel. Each receiver requests an arbitrary file from the library. The objective is to design a cache placement without knowing the receivers' requests and a communication scheme such that the sum Degrees of Freedom (sum-DoF) of the delivery is maximized. This network model has been investigated by , who proposed a prefetching and a delivery scheme that achieve a sum-DoF of min M&#60;sub&#62;T&#60;&#x002F;sub&#62; K&#60;sub&#62;T&#60;&#x002F;sub&#62; &#x002B; K&#60;sub&#62;R&#60;&#x002F;sub&#62; M&#60;sub&#62;R&#60;&#x002F;sub&#62;&#x002F;N, K&#60;sub&#62;R&#60;&#x002F;sub&#62; . One of the biggest limitations of this scheme is the requirement of high subpacketization level. This paper attempts to design new algorithms to reduce the file subpacketization in such a network. In particular, we propose a new approach for both prefetching and linear delivery based on a combinatorial design called hypercube. We show that the required number of packets per file can be exponentially reduced compared to the state-of-the-art scheme proposed by , or the NMA scheme. When M&#60;sub&#62;T&#60;&#x002F;sub&#62; K&#60;sub&#62;T&#60;&#x002F;sub&#62; &#x002B; K&#60;sub&#62;R&#60;&#x002F;sub&#62; M&#60;sub&#62;R&#60;&#x002F;sub&#62; &#x2264; K&#60;sub&#62;R&#60;&#x002F;sub&#62;, the achievable one-shot sum-DoF using this approach is M&#60;sub&#62;T&#60;&#x002F;sub&#62; K&#60;sub&#62;T&#60;&#x002F;sub&#62; &#x002B; K&#60;sub&#62;R&#60;&#x002F;sub&#62; M&#60;sub&#62;R&#60;&#x002F;sub&#62;&#x002F;N, which shows that 1) the one-shot sum-DoF scales linearly with the aggregate cache size in the network and 2) it is within a factor of 2 to the information-theoretic optimum. Surprisingly, the identical and near optimal sum-DoF performance can be achieved using the hypercube approach with a much less file subpacketization. We consider a system, comprising a library of @math files (e.g., movies) and a wireless network with a @math transmitters, each equipped with a local cache of size of @math files and a @math receivers, each equipped with a local cache of size of @math files. Each receiver will ask for one of the @math 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 @math is achievable, and this is within a factor of 2 of the optimum, under uncoded prefetching and one-shot linear delivery 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’ caches 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 transmitter’s caches to cooperatively zero-force some outgoing interference, and availability of the unintended content at the receiver’s 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. We study the role of caches in wireless interference networks. We focus on content caching and delivery across a Gaussian interference network, where both transmitters and receivers are equipped with caches. We provide a constant-factor approximation of the system's degrees of freedom (DoF), for arbitrary number of transmitters, number of receivers, content library size, receiver cache size, and transmitter cache size (as long as the transmitters combined can store the entire content library among them). We demonstrate approximate optimality with respect to information-theoretic bounds that do not impose any restrictions on the caching and delivery strategies. Our characterization reveals three key insights. First, the approximate DoF is achieved using a strategy that separates the physical and network layers. This separation architecture is thus approximately optimal. Second, we show that increasing transmitter cache memory beyond what is needed to exactly store the entire library between all transmitters does not provide more than a constant-factor benefit to the DoF. A consequence is that transmit zero-forcing is not needed for approximate optimality. Third, we derive an interesting trade-off between the receiver memory and the number of transmitters needed for approximately maximal performance. In particular, if each receiver can store a constant fraction of the content library, then only a constant number of transmitters are needed. Our solution to the caching problem requires formulating and solving a new communication problem, the symmetric multiple multicast X-channel, for which we provide an exact DoF characterization. Over the past decade, the bulk of wireless traffic has shifted from speech to content. This shift creates the opportunity to cache part of the content in memories closer to the end users, for example in base stations. Most of the prior literature focuses on the reduction of load in the backhaul and core networks due to caching, i.e., on the benefits caching offers for the wireline communication link between the origin server and the caches. In this paper, we are instead interested in the benefits caching can offer for the wireless communication link between the caches and the end users. To quantify the gains of caching for this wireless link, we consider an interference channel in which each transmitter is equipped with an isolated cache memory. Communication takes place in two phases, a content placement phase followed by a content delivery phase. The objective is to design both the placement and the delivery phases to maximize the rate in the delivery phase in response to any possible user demands. Focusing on the three-user case, we show that through careful joint design of these phases, we can reap three distinct benefits from caching: a load balancing gain, an interference cancellation gain, and an interference alignment gain. In our proposed scheme, load balancing is achieved through a specific file splitting and placement, creating a particular pattern of content overlap at the caches. This overlap allows to implement interference cancellation. Further, it allows us to construct several virtual transmitters, each responsible for a part of the requested content, which increases interference alignment possibilities. 