This work studies a well-known shared-cache coded caching scenario where each cache can serve an arbitrary number of users. We analyze the case where there is some knowledge about such number of users (i.e., the topology) during the content placement phase. Under the assumption of regular placement and a cumulative cache size that can be optimized across the different caches, we derive the fundamental limits of performance by introducing a novel cache-size optimization and placement scheme and a novel information-theoretic converse. The converse employs new index coding techniques to bypass traditional uniformity requirements, thus finely capturing the heterogeneity of the problem, and it provides a new approach to handle asymmetric settings. The new fundamental limits reveal that heterogeneous topologies can in fact outperform their homogeneous counterparts where each cache is associated to an equal number of users. These results are extended to capture the scenario of topological uncertainty where the perceived/estimated topology does not match the true network topology. This scenario is further elevated to the stochastic setting where the user-to-cache association is random and unknown, and it is shown that the proposed scheme is robust to such noisy or inexact knowledge on the topology.

Multi-antenna coded caching is known to combine a global caching gain that is proportional to the cumulative cache size found across the network, with an additional spatial multiplexing gain that stems from using multiple transmitting antennas. However, a closer look reveals two severe bottlenecks; the well-known exponential subpacketization bottleneck that dramatically reduces performance when the communicated file sizes are finite, and the considerable optimization complexity of beamforming multicast messages when the SNR is finite. We here present an entirely novel caching scheme, termedcyclic multi-antennacoded caching, whose unique structure allows for the resolution of the above bottlenecks in the crucial regime of many transmit antennas. For this regime, where the multiplexing gain can exceed the coding gain, our new algorithm is the first to achieve the exact one-shot linear optimal DoF with a subpacketization complexity that scales only linearly with the number of users, and the first to benefit from a multicasting structure that allows for exploiting uplink-downlink duality in order to yield optimized beamformers ultra-fast. In the end, our novel solution provides excellent performance for networks with finite SNR, finite file sizes, and many users.

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.

This work considers the cache-aided multiple-input single-output broadcast channel (MISO BC) where an L-antenna transmitter serves K receiving users, each assisted by one of ΛKγ, all existing coded caching schemes suffer substantially reduced caching or multiplexing gains. Our work provides a novel coded caching scheme that achieves the exact best known, near optimal, DoF L+Kγ, and does so even if L > Kγ, thus covering an important hole in identifying the optimal performance for the multi-antenna shared-cache problem. Therefore, our work reveals that shared-cache systems with many transmit antennas can also enjoy both full multiplexing gains (L) as well as full caching gains (Kγ) despite the sharing of the caches. A side benefit of this scheme is its applicability in multi-antenna settings with dedicated users caches, where it can offer the advantage of reducing the subpacketization without sacrificing the DoF performance.

The work explores the fundamental limits of coded caching in the setting where a transmitter with potentially multiple (N0) antennas serves different users that are assisted by a smaller number of caches. Under the assumption of uncoded cache placement, the work derives the exact optimal worst-case delay and DoF, for a broad range of user-to-cache association profiles where each such profile describes how many users are helped by each cache. This is achieved by presenting an information-theoretic converse based on index coding that succinctly captures the impact of the user-to-cache association, as well as by presenting a coded caching scheme that optimally adapts to the association profile by exploiting the benefits of encoding across users that share the same cache. The work reveals a powerful interplay between shared caches and multiple senders/antennas, where we can now draw the striking conclusion that, as long as each cache serves at least N0users, adding a single degree of cache-redundancy can yield a DoF increase equal to N0, while at the same time - irrespective of the profile - going from 1 to N0antennas reduces the delivery time by a factor of N0. Finally some conclusions are also drawn for the related problem of coded caching with multiple file requests.

The work studies the K -user shared-link broadcast channel with coded caching, where each user's file-request comes with a certain Quality-of-Service (QoS) requirement, thus allowing - in the context of multi-layered coding - users to download only those file layers that are necessary to meet their own QoS requirements. The work characterizes the exact optimal worst-case delivery time, under the assumption of uncoded cache placement that is oblivious to the individual QoS requirement of each user. The work derives a new index coding based information theoretic converse, which interestingly tells us exactly how to optimally cache.

This work studies the K-user broadcast channel where each user is assisted by one of Λ caches with a cumulative memory constraint that is equal to t times the size of the library, and where each cache serves an arbitrary number of users. In this setting, under the assumption of uncoded cache placement, no prior scheme is known to achieve a sum degrees of freedom (DoF) of t + 1, other than in the uniform case where all caches serve an equal number of users. We here show for the first time that allowing an optimized memory allocation across the caches as a function of the number of users served per cache, provides for the aforementioned DoF. A subsequent index-coding based converse proves that this performance can be close to optimal for bounded values of t.

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.

This work explores a distributed computing setting where K nodes are assigned fractions (subtasks) of a computational task in order to perform the computation in parallel. In this setting, a well-known main bottleneck has been the internode communication cost required to parallelize the task, because unlike the computational cost which could keep decreasing as K increases, the communication cost remains approximately constant, thus bounding the total speedup gains associated to having more computing nodes. This bottleneck was substantially ameliorated by the recent introduction of coded techniques in the context of MapReduce which allowed each node - at the computational cost of having to preprocess approximately t times more subtasks - to reduce its communication cost by approximately t times. In reality though, the associated speed up gains were severely limited by the requirement that larger t and K necessited that the original task be divided into an extremely large number of subtasks. In this work we show how node cooperation, along with a novel assignment of tasks, can help to dramatically ameliorate this limitation. The result applies to wired as well as wireless distributed computing and it is based on the idea of having groups of nodes compute identical mapping tasks and then employing a here-proposed novel D2D coded caching algorithm. In this context, the new approach here manages to achieve a virtual decomposition of the fully connected D2D setting into parallel ones, which significantly reduces the required subpacketization.

In the context of caching in heterogeneous networks, the work explores the setting where a multi-antenna transmitter (No antennas), broadcasts to K receiving users, each assisted by one of Λ ≤ K helper nodes serving as limited-sized caches. Our aim is to identify the limits of coded caching when there are fewer caches than users (Λ0, adding a single degree of cache-redundancy yields a caching-gain increase equal to No, and similarly, adding antennas has a multiplicative DoF impact where for example introducing a second transmit antenna can double the DoF.

Fault injection attacks are a powerful tool to exploit implementative weaknesses of robust cryptographic algorithms. The faults induced during the computation of the cryptographic primitives allow to extract pieces of information about the secret parameters stored into the device using the erroneous results. Various fault induction techniques have been researched, both to make practical several theoretical fault models proposed in open literature and to outline new kinds of vulnerabilities. In this paper we describe a non-invasive fault model based on the effects of underfeeding the power supply of an ARM general purpose CPU. We describe the methodology followed to characterize the fault model on an ARM9 microprocessor and propose and mount attacks on implementations of the RSA primitives.