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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 at the wireless edge nodes is a promising way to boost the spatial and spectral efficiency, for the sake of alleviating networks from content-related traffic. Coded caching originally introduced by Maddah-Ali and Niesen significantly speeds up communication efficiency by transmitting multicast messages simultaneously useful to multiple users. Most prior works on coded caching are based on the assumption that each user may request all content in the library. However, in many applications the users are interested only in a limited set of content that depends on their location. For example, assisted self-driving vehicles may access super High-Definition maps of the area through which they are travelling. Motivated by these considerations, this paper formulates the coded caching problem for location-based content with edge cache nodes. The considered problem includes a content server with access to ${\mathsf N}$ location-based files (e.g., High-Definition maps), ${\mathsf K}$ edge cache nodes located at different regions, and ${\mathsf K}$ users (i.e., vehicles) each of which is in the serving region of one cache node and can retrieve the cached content of this cache node with negligible cost. Depending on the location, each user only requests a file from a location-dependent subset of the library. The objective is to minimize the worst-case load (i.e., the worst-case number of broadcasted bits from the content server among all possible demands). For this novel coded caching problem, we propose a highly non-trivial converse bound under uncoded cache placement (i.e., each cache node directly copies some library bits in its cache), which shows that a simple achievable scheme is optimal under uncoded cache placement. In addition, this achievable scheme is also proved to be generally order optimal within a factor of 3. Finally, we extend the coded caching problem for location-based content to the multiaccess coded caching topology originally proposed by Hachem et al., where each user is connected to ${\mathsf L}$ nearest cache nodes. When ${\mathsf L}\geq 2$ , we characterize the exact optimality on the worst-case load. [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]

This paper considers the multiaccess coded caching systems formulated by Hachem et al., including a central server containing $N$ files connected to $K$ cache-less users through an error-free shared link, and $K$ cache-nodes, each equipped with a cache memory size of $M$ files. Each user has access to $L$ neighbouring cache-nodes with a cyclic wrap-around topology. The coded caching scheme proposed by Hachem et al. suffers from the case that $L$ does not divide $K$ , where the needed number of transmissions (a.k.a. load) is at most four times the load expression for the case where $L$ divides $K$. Our main contribution is to propose a novel transformation approach to smartly extend the schemes satisfying some conditions for the well known shared-link caching systems to the multiaccess caching systems. Then we can get many coded caching schemes with different subpacketizations for multiaccess coded caching system. These resulting schemes have the maximum local caching gain (i.e., the cached contents stored at any $L$ neighbouring cache-nodes are different such that the number of retrieval packets by each user from the connected cache-nodes is maximal) and the same coded caching gain as the original schemes. Applying the transformation approach to the well-known shared-link coded caching scheme proposed by Maddah-Ali and Niesen, we obtain a new multiaccess coded caching scheme that achieves the same load as the scheme of Hachem et al. but for any system parameters. Under the constraint of the cache placement used in this new multiaccess coded caching scheme, our delivery strategy is approximately optimal when $K$ is sufficiently large. Finally, we also show that the transmission load of the proposed scheme can be further reduced by compressing the multicast message. [ABSTRACT FROM AUTHOR]

We consider the problem of cache-aided Multiuser Private Information Retrieval (MuPIR) which is an extension of the single-user cache-aided PIR problem to the case of multiple users. In cache-aided MuPIR, each of the $K_{\mathrm{ u}}$ cache-equipped users wishes to privately retrieve a message out of $K$ messages from $N$ databases each having access to the entire message library. Demand privacy requires that any individual database learns nothing about the demands of all users. The users are connected to each database via an error-free shared-link. In this paper, we aim to characterize the optimal trade-off between user cache memory and communication load for such systems. First, we propose a novel approach of cache-aided interference alignment (CIA), for the MuPIR problem with $K=2$ messages, $K_{\mathrm{ u}}=2$ users and $N\ge 2$ databases. The CIA approach is optimal when the cache placement is uncoded. For general cache placement, the CIA approach is optimal when $N=2$ and 3 verified by the computer-aided converse approach. Second, for the general case, we propose a product design (PD) which incorporates the PIR code into the linear caching code. The product design is shown to be order optimal within a multiplicative factor of 8 and is exactly optimal in the high memory regime. [ABSTRACT FROM AUTHOR]