This work elevates coded caching networks from their purely information-theoretic framework to a stochastic setting, by exploring the effect of random user activity and by exploiting correlations in the activity patterns of different users. In particular, the work studies the$K$-user cache-aided broadcast channel with a limited number of cache states (i.e., the content stored at the cache of a certain user), and explores the effect of cache state association strategies in the presence of arbitrary user activity levels; a combination that strikes at the very core of the coded caching problem and its crippling subpacketization bottleneck. We first present a statistical analysis of the average worst-case delay performance of such subpacketization-constrained (state-constrained) coded caching networks, and provide computationally efficient performance bounds as well as scaling laws for any arbitrary probability distribution of the user-activity levels. The achieved performance is a result of a novel user-to-cache state association algorithm that leverages the knowledge of probabilistic user-activity levels. We then follow a data-driven approach that exploits the prior history on user-activity levels and correlations, in order to predict interference patterns, and thus better design the caching algorithm. This optimized strategy is based on the principle that users that overlap more, interfere more, and thus have higher priority to secure complementary cache states. This strategy is proven here to be within a small constant factor from the optimal. Finally, the above analysis is validated numerically using synthetic data following the Pareto principle. To the best of our understanding, this is the first work that seeks to exploit user-activity levels and correlations, in order to map future interference and design optimized coded caching algorithms that better handle this interference.

This work presents a new way of exploiting non-uniform file popularity in coded caching networks. Focusing on a fully-connected fully-interfering wireless setting with multiple cache-enabled transmitters and receivers, we show how non-uniform file popularity can be used very efficiently to accelerate the impact of transmitter-side data redundancy on receiver-side coded caching. This approach is motivated by the recent discovery that, under any realistic file-size constraint, having content appear in multiple transmitters can in fact dramatically boost the speed-up factor attributed to coded caching. We formulate an optimization problem that exploits file popularity to optimize the placement of files at the transmitters. Consequently, we propose a search algorithm that solves the problem at hand while reducing the variable search space significantly. We also prove an analytical performance upper bound, which is in fact met by our algorithm in the regime of many receivers. Our work reflects the benefits of allocating higher cache redundancy to more popular files, but also reflects a law of diminishing returns where for example very popular files may in fact benefit from minimum redundancy. In the end, this work reveals that in the context of coded caching, employing multiple transmitters can be a catalyst in fully exploiting file popularity, as it avoids various asymmetry complications that appear when file popularity is used to alter the receiver-side cache placement.

This work studies the K-user broadcast channel with Λ caches, when the association between users and caches is random, i.e., for the scenario where each user can appear within the coverage area of – and subsequently is assisted by – a specific cache based on a given probability distribution. Caches are subject to a cumulative memory constraint that is equal to t times the size of the library. We provide a scheme that consists of three phases: the storage allocation phase, the content placement phase, and the delivery phase, and show that an optimized storage allocation across the caches together with a modified uncoded cache placement and delivery strategy alleviates the adverse effect of cache-load imbalance by significantly reducing the multiplicative performance deterioration due to randomness. In a nutshell, our work provides a scheme that manages to substantially mitigate the impact of cache-load imbalance in stochastic networks, as well as – compared to the best known state-of-the-art – the well-known subpacketization bottleneck by showing its applicability in deterministic settings for which it achieves the same delivery time – which was proven to be close to optimal for bounded values of t – with an exponential reduction in the subpacketization.

This work proposes a two-layered coded caching scheme to resolve the cache-load imbalance bottleneck of the coded caching in a stochastic shared-cache network where the association between users and shared caches is random, i.e., for the scenario where each user can appear within the coverage area of – and subsequently is assisted by – a specific cache-enabled helper node based on a uniform probability distribution. To insightfully capture the effectiveness of our scheme in mitigating the adverse effect of randomness in shared-cache networks, we derive the exact scaling laws of the average delivery time. In the scenario of an error-free broadcast channel of bounded capacity per unit of time where the delivery involves K users and Λ cache-enabled helper nodes, we show that empowering users with an additional layer of caching can significantly mitigate, and in certain memory regimes completely nullify the adverse effects of the cache-load imbalance bottleneck.

The work establishes the exact performance limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. Under the premise that more balanced user-to-cache associations perform better than unbalanced ones, our work provides a statistical analysis of the average performance of such networks, identifying in closed form, the exact optimal average delivery time. To insightfully capture this delay, we derive easy-to-compute closed-form analytical bounds that prove tight in the limit of a large number Λ of cache states. In the scenario where delivery involves K users, we conclude that the multiplicative performance deterioration due to randomness - as compared to the well-known deterministic uniform case - can be unbounded and can scale as Θ([log Λ]/[log log Λ]) at K = Θ(Λ ), and that this scaling vanishes when K = Ω(Λ log Λ ). To alleviate this adverse effect of cache-load imbalance, we consider various load-balancing methods, and show that employing proximity-bounded load balancing with an ability to choose from h neighboring caches, the aforementioned scaling reduces to Θ([log(Λ/h)]/[log log(Λ/h)]) at K=Θ(Λ ), while when the proximity constraint is removed, the scaling is of a much slower order Θ(log log Λ ). The above analysis is extensively validated numerically.

The work establishes the exact fundamental limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. This association can greatly affect performance, which improves when the association is more balanced across the caches, and which deteriorates when this association becomes less uniform. Our work provides a statistical analysis of the average performance of such networks, quantifying the effect of randomness by identifying in closed-form, the exact optimal average delivery time. To insightfully capture this delay, we derive the exact scaling laws of the optimal average delivery time. In the scenario where delivery involves K users, we conclude that the multiplicative performance deterioration due to randomness - as compared to the well-known deterministic uniform case - can be unbounded and can scale as Θ([(logΛ )/(loglogΛ )]) at K=Θ(Λ), and that as K increases, this deterioration gradually reduces, and ceases to scale when K=Ω(ΛlogΛ). The above analysis is validated numerically.

The work considers the K-user cache-aided sharedlink broadcast channel where each user has access to exactly z caches of normalized size γ, and where each cache assists exactly z users. For this setting, for two opposing memory regimes, we propose novel caching and coded delivery schemes which maximize the local caching gain, and achieve a coding gain larger than 1+Kγ (users served at a time) despite the fact that the total cache redundancy remains Kγ irrespective of z. Interestingly, when z = (κ-1)/(Kγ), the derived optimal coding gain is Kγz + 1, matching the performance of a hypothetical scenario where each user has its own dedicated cache of size zγ.

We consider caching of video streams in a cellular network in which each base station is equipped with a cache. Video streams are partitioned into multiple substreams and the goal is to place substreams in caches such that the residual backhaul load is minimized. We consider two coding mechanisms for the substreams: Layered coding (LC) mechanism and multiple description coding (MDC). We develop a distributed asynchronous algorithm for deciding which files to store in which cache to minimize the residual bandwidth, i.e., the cost for downloading the missing substreams of the user's requested video with a certain video quality from the gateway (i.e., the main server). We show that our algorithm converges rapidly. Finally, we show that MDC partitioning is better than the LC mechanism when the most popular content is stored in caches; however, our algorithm enables to use the LC mechanism as well without any performance loss.

In this work we investigate optimal geographical caching in heterogeneous cellular networks where different types of base stations (BSs) have different cache capacities. Users request files from a content library according to a known probability distribution. The performance metric is the total hit probability, which is the probability that a user at an arbitrary location in the plane will find the content that it requires in one of the BSs that it is covered by. We consider the problem of optimally placing content in all BSs jointly. As this problem is not convex, we provide a heuristic scheme by finding the optimal placement policy for one type of base station conditioned on the placement in all other types. We demonstrate that these individual optimization problems are convex and we provide an analytical solution. As an illustration, we find the optimal placement policy of the small base stations (SBSs) depending on the placement policy of the macro base stations (MBSs). We show how the hit probability evolves as the deployment density of the SBSs varies. We show that the heuristic of placing the most popular content in the MBSs is almost optimal after deploying the SBSs with optimal placement policies. Also, for the SBSs no such heuristic can be used; the optimal placement is significantly better than storing the most popular content. Finally, we show that solving the individual problems to find the optimal placement policies for different types of BSs iteratively, namely repeatedly updating the placement policies, does not improve the performance.

Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2 × 2 generator matrix, polarises the channels, that is, a portion of the channel capacities approach 1, whereas the remaining channel capacities approach 0. Owing to the specific size of this original generator matrix, polar codes can only have code lengths equal to the powers of 2, resulting in inefficiency for codes of practical lengths. In this study, the performance of finite‐length polar codes over the binary erasure channel is analysed. A normalised polarisation distance measure is defined and polar codes from different generator matrices showing different amount of polarisation are compared using this measure. Encoding structures for these generalised polar codes are proposed and polarisation performances in both asymptotical and finite‐length cases are investigated for generator matrices of size 3 × 3 and 4 × 4. A generalised decoder is also proposed for this generator matrix and its erasure rate is compared with that of the original generator matrix. It is shown that polar codes that have performance similar to the original construction can be constructed and used for a variety of code lengths, not necessarily equal to powers of 2, using generalised generator matrices.