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In the coded caching problem, as originally formulated by Maddah-Ali and Niesen, a server communicates via a noiseless shared broadcast link to multiple users that have local storage capability. In order for a user to decode its demanded file from the coded multicast transmission, the demands of all the users must be globally known, which may violate the privacy of the users. To overcome this privacy problem, Wan and Caire recently proposed several schemes that attain coded multicasting gain while simultaneously guarantee information theoretic privacy of the users’ demands. In Device-to-Device (D2D) networks, the demand privacy problem is further exacerbated by the fact that each user is also a transmitter, which appears to be needing the knowledge of the files demanded by the remaining users in order to form its coded multicast transmission. This paper shows how to solve this seemingly infeasible problem. The main contribution of this paper is the development of new achievable and converse bounds for D2D coded caching that are to within a constant factor of one another when privacy of the users’ demands must be guaranteed even in the presence of colluding users (i.e., when some users share cached contents and demanded file indices). First, a D2D private caching scheme is proposed, whose key feature is the addition of virtual users in the system in order to “hide” the demands of the real users. By comparing the achievable D2D private load with an existing converse bound for the shared-link model without demand privacy constraint, the proposed scheme is shown to be order optimal, except for the very low memory size regime with more files than users. Second, in order to shed light into the open parameter regime, a new achievable scheme and a new converse bound under the constraint of uncoded cache placement (i.e., when each user stores directly a subset of the bits of the library) are developed for the case of two users, and shown to be to within a constant factor of one another for all system parameters. Finally, the two-user converse bound is extended to any number of users by a cut-set type argument. With this new converse bound, the virtual users scheme is shown to be order optimal in all parameter regimes under the constraint of uncoded cache placement and user collusion. [ABSTRACT FROM AUTHOR]

Coded caching is a promising technique to smooth out network traffic by storing part of the library content at the users’ local caches. The seminal work on coded caching for single file retrieval by Maddah-Ali and Niesen (MAN) showed the existence of a global caching gain that scales with the total memory in the system, in addition to the known local caching gain in uncoded systems. This paper formulates a novel cache-aided matrix multiplication retrieval problem, relevant for data analytics and machine learning applications. In the considered problem, each cache-aided user requests the product of two matrices from the library. A structure-agnostic solution is to treat each possible matrix product as an independent file and use the MAN coded caching scheme for single file retrieval. This paper proposes two structure-aware schemes, which partition each matrix in the library by either rows or columns and let a subset of users cache some sub-matrices, that improve on the structure-agnostic scheme. For the case where the library matrices are “fat” matrices, the structure-aware row-partition scheme is shown to be order optimal under some constraint. [ABSTRACT FROM AUTHOR]

Caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the users’ local caches. For the shared-link network with end-user-caches, Maddah-Ali and Niesen proposed a two-phase coded caching strategy. In practice, users may communicate with the server through intermediate relays. This paper studies the tradeoff between the memory size ${\mathsf M}$ and the network load ${\mathsf R}$ for the networks where a server with ${\mathsf N}$ files is connected to ${\mathsf H}$ relays (without caches), which in turn are connected to ${\mathsf K}$ users equipped with caches of ${\mathsf M}$ files. When each user is connected to a different subset of ${\mathsf r}$ relays, i.e., ${\mathsf K}= \binom {\mathsf H}{\mathsf r}$ , the system is referred to as a combination network with end-user-caches. In this work, converse bounds are derived for the practically motivated case of uncoded cache contents, that is, bits of the various files are directly pushed into the user caches without any coding. In this case, once the cache contents and the users’ demands are known, the problem reduces to a general index coding problem. This paper shows that relying on a well-known “acyclic index coding converse bound” results in converse bounds that are not tight for combination networks with end-user-caches. A novel converse bound that leverages the network topology is proposed, which is the tightest converse bound known to date. As a result of independent interest, an inequality that generalizes the well-known sub-modularity of entropy is derived. Several novel caching schemes are proposed, based on the Maddah-Ali and Niesen cache placement. These schemes leverage the structure of the combination network or/and perform interference elimination at the end-users. The proposed schemes are proved: (i) to be (order) optimal for some $({\mathsf N}, {\mathsf M}, {\mathsf H}, {\mathsf r})$ parameters regimes under the constraint of uncoded cache placement, and (ii) to outperform the state-of-the-art schemes in numerical evaluations. [ABSTRACT FROM AUTHOR]

Coded caching has the potential to greatly reduce network traffic by leveraging the cheap and abundant storage available in end-user devices so as to create multicast opportunities in the delivery phase. In the seminal work by Maddah-Ali and Niesen (MAN), the shared-link coded caching problem was formulated, where each user demands one file (i.e., single file retrieval). This article generalizes the MAN caching problem formulation from single file retrieval on the binary filed to general scalar linear function retrieval on an arbitrary finite field. The proposed novel scheme is linear, based on MAN uncoded cache placement, and leverages ideas from interference alignment. Quite surprisingly, the worst-case load of the proposed scheme among all possible demands is the same as the one of the scheme by Yu, Maddah-Ali, and Avestimehr (YMA) for single file retrieval. The proposed scheme has thus the same optimality guarantees as YMA, namely, it is optimal under the constraint of uncoded cache placement, and is optimal to within a factor 2 otherwise. Some extensions of the proposed scheme are then discussed. It is shown that the proposed scheme works not only on arbitrary finite field, but also on any commutative ring. The key idea of this article can be also extended to all scenarios to which the original MAN scheme has been extended, including but not limited to demand-private retrieval and Device-to-Device networks. [ABSTRACT FROM AUTHOR]

Maddah-Ali and Niesen (MAN) in 2014 showed that coded caching in single bottleneck-link broadcast networks allows serving an arbitrarily large number of cache-equipped users with a total link load (bits per unit time) that does not scale with the number of users. Since then, the general topic of coded caching has generated enormous interest both from the information theoretic and (network) coding theoretic viewpoint, and from the viewpoint of applications. Building on the MAN work, this paper considers a particular network topology referred to as cache-aided Fog Radio Access Network (Fog-RAN), that includes a Macro-cell Base Station (MBS) co-located with the content server, several cache-equipped Small-cell Base Stations (SBSs), and many users without caches. Some users are served directly by the MBS broadcast downlink, while other users are served by the SBSs. The SBSs can also exchange data via rounds of direct communication via a side channel, referred to as “sidelink”. For this novel Fog-RAN model, the fundamental tradeoff among (a) the amount of cache memory at the SBSs, (b) the load on the downlink (from MBS to directly served users and SBSs), and (c) the aggregate load on the sidelink is studied, under the standard worst-case demand scenario. We propose a converse bound whose key novelty is to jointly bound the downlink load an the sidelink load. For the achievability, by leveraging the network topology, we propose two classes of memory-loads point, where the SBS sidelink load is minimum and the MBS downlink load is minimum, respectively. By memory-sharing between these two classes of memory-loads points, some exact or order optimality results are obtained. Several existing models (e.g., Device-to-Device coded caching, single bottleneck-link coded caching with shared caches, single bottleneck-link caching coded caching with cache-less users) are recovered as special cases of this network model and by-product results of independent interest are given. Finally, the role of topology-aware versus topology-agnostic caching is discussed. [ABSTRACT FROM AUTHOR]

Caching is an efficient way to reduce network traffic congestion during peak hours, by storing some content at the user’s local cache memory, even without knowledge of user’s later demands. Maddah-Ali and Niesen proposed a two-phase (placement phase and delivery phase) coded caching strategy for broadcast channels with cache-aided users. This paper investigates the same model under the constraint that content is placed uncoded within the caches, that is, when bits of the files are simply copied within the caches. When the cache contents are uncoded and the users’ demands are revealed, the caching problem can be connected to an index coding problem. This paper focuses on deriving fundamental performance limits for the caching problem by using tools for the index coding problem that were either known or are newly developed in this work. First, a converse bound for the caching problem under the constraint of uncoded cache placement is proposed based on the “acyclic index coding converse bound.” This converse bound is proved to be achievable by the Maddah-Ali and Niesen’s scheme when the number of files is not less than the number of users, and by a newly derived index coding achievable scheme otherwise. The proposed index coding achievable scheme is based on distributed source coding and strictly improves on the widely used “composite (index) coding” achievable bound and its improvements, and is of independent interest. An important consequence of the findings of this paper is that advancements on the coded caching problem posed by Maddah-Ali and Niesen are thus only possible by considering strategies with coded placement phase. A recent work by Yu et al has however shown that coded cache placement can at most half the network load compared to the results presented in this paper. [ABSTRACT FROM AUTHOR]