We propose a novel caching strategy for the problem of centralized coded caching with non-uniform demands. Our placement strategy can be applied to an arbitrary number of users and files, and can be easily adapted to the scenario where file popularities are user-specific. The distinguishing feature of the proposed placement strategy is that it allows for equal sub-packetization for all files while requiring the users to allocate more cache to the more popular files. This creates natural broadcasting opportunities in the delivery phase which are simultaneously helpful for users who have requested files of different popularities. For the case of two files, we propose a delivery strategy which meets a natural extension of the existing converse bounds under uncoded placement to non-uniform demands, thereby establishing the optimal expected memory-rate trade-off for the case of two files with arbitrary popularities under the restriction of uncoded placement.
Replicating or caching popular content in memories distributed across the network is a technique to reduce peak network loads. Conventionally, the main performance gain of this caching was thought to result from making part of the requested data available closer to end-users. Instead, we recently showed that a much more significant gain can be achieved by using caches to create coded-multicasting opportunities, even for users with different demands, through coding across data streams. These coded-multicasting opportunities are enabled by careful content overlap at the various caches in the network, created by a central coordinating server. In many scenarios, such a central coordinating server may not be available, raising the question if this multicasting gain can still be achieved in a more decentralized setting. In this paper, we propose an efficient caching scheme, in which the content placement is performed in a decentralized manner. In other words, no coordination is required for the content placement. Despite this lack of coordination, the proposed scheme is nevertheless able to create coded-multicasting opportunities and achieves a rate close to the optimal centralized scheme. We consider the canonical shared link caching network formed by a source node, hosting a library of @math information messages (files), connected via a noiseless multicast link to @math user nodes, each equipped with a cache of size @math files. Users request files independently at random according to an a-priori known demand distribution q. A coding scheme for this network consists of two phases: cache placement and delivery. The cache placement is a mapping of the library files onto the user caches that can be optimized as a function of the demand statistics, but is agnostic of the actual demand realization. After the user demands are revealed, during the delivery phase the source sends a codeword (function of the library files, cache placement, and demands) to the users, such that each user retrieves its requested file with arbitrarily high probability. The goal is to minimize the average transmission length of the delivery phase, referred to as rate (expressed in channel symbols per file). In the case of deterministic demands, the optimal min-max rate has been characterized within a constant multiplicative factor, independent of the network parameters. The case of random demands was previously addressed by applying the order-optimal min-max scheme separately within groups of files requested with similar probability. However, no complete characterization of order-optimality was previously provided for random demands under the average rate performance criterion. In this paper, we consider the random demand setting and, for the special yet relevant case of a Zipf demand distribution, we provide a comprehensive characterization of the order-optimal rate for all regimes of the system parameters, as well as an explicit placement and delivery scheme achieving order-optimal rates. We present also numerical results that confirm the superiority of our scheme with respect to previously proposed schemes for the same setting. Caching plays an important role in reducing the backbone traffic when serving high-volume multimedia content. Recently, a new class of coded caching schemes have received significant interest, because they can exploit coded multi-cast opportunities to further reduce backbone traffic. Without considering file popularity, prior works have characterized the fundamental performance limits of coded caching through a deterministic worst-case analysis. However, when heterogeneous file popularity is considered, there remain open questions regarding the fundamental limits of coded caching performance. In this paper, for an arbitrary popularity distribution, we first derive a new information-theoretic lower bound on the expected transmission rate of any coded caching schemes. We then show that a simple coded-caching scheme attains an expected transmission rate that is at most a constant factor away from the lower bound. Unlike other existing studies, the constant factor that we derived is independent of the popularity distribution. We consider a network consisting of a file server connected through a shared link to a number of users, each equipped with a cache. Knowing the popularity distribution of the files, the goal is to optimally populate the caches, such as to minimize the expected load of the shared link. For a single cache, it is well known that storing the most popular files is optimal in this setting. However, we show here that this is no longer the case for multiple caches. Indeed, caching only the most popular files can be highly suboptimal. Instead, a fundamentally different approach is needed, in which the cache contents are used as side information for coded communication over the shared link. We propose such a coded caching scheme and prove that it is close to optimal. For a network with one sender, n receivers (users) and m possible messages (files), caching side information at the users allows to satisfy arbitrary simultaneous demands by sending a common (multicast) coded message. In the worst-case demand setting, explicit deterministic and random caching strategies and explicit linear coding schemes have been shown to be order optimal. In this work, we consider the same scenario where the user demands are random i.i.d., according to a Zipf popularity distribution. In this case, we pose the problem in terms of the minimum average number of equivalent message transmissions. We present a novel decentralized random caching placement and a coded delivery scheme which are shown to achieve order-optimal performance. As a matter of fact, this is the first order-optimal result for the caching and coded multicasting problem in the case of random demands.