Uncoded Caching Research Articles

Fundamental Limits of Coded Caching in Request-Robust D2D Communication Networks.

D2D coded caching, originally introduced by Ji, Caire, and Molisch, significantly improves communication efficiency by applying the multi-cast technology proposed by Maddah-Ali and Niesen to the D2D network. Most prior works on D2D coded caching are based on the assumption that all users will request content at the beginning of the delivery phase. However, in practice, this is often not the case. Motivated by this consideration, this paper formulates a new problem called request-robust D2D coded caching. The considered problem includes K users and a content server with access to N files. Only r users, known as requesters, request a file each at the beginning of the delivery phase. The objective is to minimize the average and worst-case delivery rate, i.e., the average and worst-case number of broadcast bits from all users among all possible demands. For this novel D2D coded caching problem, we propose a scheme based on uncoded cache placement and exploiting common demands and one-shot delivery. We also propose information-theoretic converse results under the assumption of uncoded cache placement. Furthermore, we adapt the scheme proposed by Yapar et al. for uncoded cache placement and one-shot delivery to the request-robust D2D coded caching problem and prove that the performance of the adapted scheme is order optimal within a factor of two under uncoded cache placement and within a factor of four in general. Finally, through numerical evaluations, we show that the proposed scheme outperforms known D2D coded caching schemes applied to the request-robust scenario for most cache size ranges.

Multi-Antenna Coded Caching for Shared Caches With Arbitrary User-to-Cache Association

We consider the multi-antenna shared cache setup where the server is equipped with multiple transmit antennas and is connected to a set of users that are assisted with a smaller number of helper nodes. The helper nodes serve as caches that are shared among the users. Each user gets connected to exactly one helper cache. For this setting, under uncoded cache placement, an optimal multi-antenna coded caching scheme supporting all types of user-to-cache association is known in the literature which is applicable only when the number of antennas is at most the number of users connected to the least occupied cache. The other known multi-antenna shared caching schemes considered only uniform association of users to helper caches. In this work, we propose a multi-antenna coded caching scheme for the shared cache setting with more diverse user-to-cache associations where the number of antennas is not less than the number of users connected to the least occupied cache. Under certain scenarios, our scheme achieves the same performance exhibited by some optimal schemes.

Fundamental Limits of Cache-Aided MIMO Wireless Networks

This paper studies the Multi-Input-Multi-Output (MIMO) interference networks with arbitrary number of transmitters and receivers, where both the transmitters and receivers are equipped with caches. The main goal is to design content placement and delivery schemes that minimize the worst case normalized delivery time (NDT). First, we propose a delivery scheme for the cache-aided Single-Input-Multiple-Output (SIMO) interference networks. Then, we obtain the achievable NDT of the cache-aided MIMO interference networks using the decomposition property of splitting each multi-antenna transmitter into multiple single antenna transmitters. Furthermore, we derive an information-theoretic bound on the optimal NDT of the cache-aided MIMO interference network. Analytical results show that the proposed scheme is within a multiplicative gap of 2 from the derived lower bound independent of all system parameters for any uncoded cache placement scheme. We also derive a novel delivery scheme for the cache-aided Multi-Input-Single-Output (MISO) interference network outperforming our proposed scheme for the cache-aided MIMO interference network. The numerical results show the superiority of our proposed scheme over the state-of-the-art schemes in the literature. Our results show that the coded caching gain has a more significant contribution in reducing the transmission latency than the spatial multiplexing gain. Our results indicate that the receive-antennas become more effective in reducing the NDT than the transmit-antennas in the presence of caches at the receiver-side. In addition, we show that increasing the number of transmit-antennas has a higher gain in reducing the NDT than adding more transmitters in the cache-aided MISO interference network.

On the Computational Aspect of Coded Caching With Uncoded Prefetching

Coded caching is the distribution of content across a communication system using techniques from coding theory in order to create multicasting opportunities among the users receiving the content. This enables a multiplicative improvement over the classic uncoded caching with respect to the transmission rates required in the delivery phase of the content. Since its introduction, coded caching has eliceted significant research interest as a result of which several different schemes have been proposed over the last few years. This work focuses on the fundamental case of coded caching with uncoded prefetching. In this case, the users’ caches are filled with uncoded content during a prefetching phase in order to best serve the request made by each user during a subsequent delivery phase. This important case has recently received a complete information-theoretic characterization. However, reaching the information-theoretic optimality imposes a significant computational imbalance among the users. To mitigate this imbalance, we perform a complete computational analysis of the two major forms of coded caching with uncoded prefetching, namely centralized and decentralized. Furthermore, we propose a new information-theoretically optimal method for the delivery phase that achieves a significant computational improvement compared to the state of the art.

Memory-Rate Tradeoff for Caching With Uncoded Placement Under Nonuniform Random Demands

For a caching system with multiple users, we aim to characterize the memory-rate tradeoff for caching with uncoded cache placement, under nonuniform file popularity. Focusing on the modified coded caching scheme (MCCS) recently proposed by Yu, etal., we formulate the cache placement optimization problem for the MCCS to minimize the average delivery rate under nonuniform file popularity, restricting to a class of popularity-first placements. We then present two information-theoretic lower bounds on the average rate for caching with uncoded placement, one for general cache placements and the other restricted to the popularity-first placements. By comparing the average rate of the optimized MCCS with the lower bounds, we prove that the optimized MCCS attains the general lower bound for the two-user case, providing the exact memory-rate tradeoff. Furthermore, it attains the popularity-first-based lower bound for the case of general K users with distinct file requests. In these two cases, our results also reveal that the popularity-first placement is optimal for the MCCS, and zero-padding used in coded delivery incurs no loss of optimality. For the case of K users with redundant file requests, our analysis shows that there may exist a gap between the optimized MCCS and the lower bounds due to zero-padding. We next fully characterize the optimal popularity-first cache placement for the MCCS, which is shown to possess a simple file-grouping structure and can be computed via an efficient algorithm using closed-form expressions. Finally, we extend our study to accommodate both nonuniform file popularity and sizes, where we show that the optimized MCCS attains the lower bound for the two-user case, providing the exact memory-rate tradeoff. Numerical results show that, for general settings, the gap between the optimized MCCS and the lower bound only exists in limited cases and is very small.

Index Coding Algorithms: Cooperative Caching and Delivery for F-RANs

In a Fog Radio Access Network (F-RAN), fog access points (F-APs) are equipped with caches that can store popular files during off-peak hours. Besides, they are densely deployed to have overlapping radio coverage so that requested files can be delivered cooperatively using beamforming. The bottleneck of the network is typically in the bandwidth-limited wireless fronthaul, which connects a cloud server to the F-APs. This work studies index coding design for cooperative caching and delivery in F-RAN to minimize fronthaul traffic and transmit energy. Index coding algorithms are designed considering the cached content at the F-APs and the possibility of beamforming in the access network under coded and uncoded caching schemes. An optimal polynomial-time index coding algorithm for uncoded and repetition caching and an efficient heuristic for Maximum Distance Separable (MDS) coded caching are designed, and their superior performance is verified by simulations. The study is further extended to consider the tradeoff between the traffic load of the fronthaul link and the transmit energy consumed in the access network. At the expense of more fronthaul traffic, beamforming opportunities can be increased, significantly reducing energy consumption. Algorithms to achieve the tradeoff are crafted, and simulation results show that uncoded caching well balances the tradeoff.

Uncoded Caching and Cross-Level Coded Delivery for Non-Uniform File Popularity

Proactive content caching at user devices and coded delivery is studied for a non-uniform file popularity distribution. A novel centralized uncoded caching and coded delivery scheme, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cross-level coded delivery (CLCD)</i> , is proposed, which can be applied to large file libraries under non-uniform demands. In the CLCD scheme, the same sub-packetization is used for all the files in the library in order to prevent additional zero-padding in the delivery phase, and unlike the existing schemes in the literature, users requesting files from different popularity groups can still be served by the same multicast message in order to reduce the delivery rate. Simulation results indicate more than 10% reduction in the average delivery rate for typical Zipf distribution parameter values.

Fundamental Structure of Optimal Cache Placement for Coded Caching With Nonuniform Demands

This paper studies the caching system of multiple cache-enabled users with random demands. Under nonuniform file popularity, we thoroughly characterize the optimal uncoded cache placement structure for the coded caching scheme (CCS). Formulating the cache placement as an optimization problem to minimize the average delivery rate, we identify the file group structure in the optimal solution. We show that, regardless of the file popularity distribution, there are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">at most three file groups</i> in the optimal cache placement, where files within a group have the same cache placement. We further characterize the complete structure of the optimal cache placement and obtain the closed-form solution in each of the three file group structures. A simple algorithm is developed to obtain the final optimal cache placement by comparing a set of candidate closed-form solutions computed in parallel. We provide insight into the file groups formed by the optimal cache placement. The optimal placement solution also indicates that coding between file groups may be explored during delivery, in contrast to the existing suboptimal file grouping schemes. Using the file group structure in the optimal cache placement for the CCS, we propose a new information-theoretic converse bound for coded caching that is tighter than the existing best one. Moreover, we characterize the file subpacketization in the CCS with the optimal cache placement solution and show that the maximum subpacketization level in the worst case scales as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ O}}(2^{K}/\sqrt {K})$ </tex-math></inline-formula> for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> users.

On the Fundamental Limits of Device-to-Device Private Caching Under Uncoded Cache Placement and User Collusion

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.

A General Coded Caching Scheme for Scalar Linear Function Retrieval

Coded caching aims to minimize the network’s peak-time communication load by leveraging the information pre-stored in the local caches at the users. The original setting by Maddah-Ali and Niesen, which considered single file retrieval, has been recently extended to general Scalar Linear Function Retrieval (SLFR) by Wan <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , who proposed a linear scheme that surprisingly achieves the same optimal load under the constraint of uncoded cache placement as in single file retrieval. This paper’s goal is to characterize the conditions under which a general SLFR linear scheme is optimal and gain insights into why the specific choices made by Wan <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> work. This paper shows that the optimal decoding coefficients are necessarily the product of two terms, one only involving the encoding coefficients and the other only the demands of the users. In addition, the algebraic relationships among the encoding coefficients of an optimal code are shown to be captured by the cycles of a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">universal graph</i> . Thus, a general linear scheme for the SLFR problem can be found by solving a spanning tree problem for the universal graph. The proposed framework readily extends to caching-like problems, such as the problem of finding a general linear scheme for Sun <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> ’s private function computation.

On the Optimal Memory-Load Tradeoff of Coded Caching for Location-Based Content

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 <inline-formula> <tex-math notation="LaTeX">${\mathsf N}$ </tex-math></inline-formula> location-based files (e.g., High-Definition maps), <inline-formula> <tex-math notation="LaTeX">${\mathsf K}$ </tex-math></inline-formula> edge cache nodes located at different regions, and <inline-formula> <tex-math notation="LaTeX">${\mathsf K}$ </tex-math></inline-formula> 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 <i>et al.</i>, where each user is connected to <inline-formula> <tex-math notation="LaTeX">${\mathsf L}$ </tex-math></inline-formula> nearest cache nodes. When <inline-formula> <tex-math notation="LaTeX">${\mathsf L}\geq 2$ </tex-math></inline-formula>, we characterize the exact optimality on the worst-case load.

Combination Networks With End-User-Caches: Novel Achievable and Converse Bounds Under Uncoded Cache Placement

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 M and the network load R for the networks where a server with N files is connected to H relays (without caches), which in turn are connected to K users equipped with caches of M files. When each user is connected to a different subset of r relays, i.e., K = (Hr), 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 (N, M, H, r) parameters regimes under the constraint of uncoded cache placement, and (ii) to outperform the state-of-the-art schemes in numerical evaluations.

Content caching for shared medium networks under heterogeneous users’ behaviors

Content caching is a widely studied technique aimed to reduce the network load imposed by data transmission during peak time while ensuring users’ quality of experience. It has been shown that when there is a common link between caches and the server, delivering contents via the coded caching scheme can significantly improve performance over conventional caching. However, finding the optimal content placement is a challenge in the case of heterogeneous users’ behaviors. In this paper we consider heterogeneous number of demands and non-uniform content popularity distribution in the case of homogeneous and heterogeneous user-preferences. We propose a hybrid coded–uncoded caching scheme to trade-off between popularity and diversity. We derive explicit closed-form expressions of the server load for the proposed hybrid scheme and formulate the corresponding optimization problem. Results show that the proposed hybrid caching scheme can reduce the server load significantly and outperforms the baseline pure coded and pure uncoded schemes and previous works in the literature for both homogeneous and heterogeneous user preferences.

Cache-Aided General Linear Function Retrieval.

Coded Caching, proposed by Maddah-Ali and Niesen (MAN), has the potential to reduce network traffic by pre-storing content in the users’ local memories when the network is underutilized and transmitting coded multicast messages that simultaneously benefit many users at once during peak-hour times. This paper considers the linear function retrieval version of the original coded caching setting, where users are interested in retrieving a number of linear combinations of the data points stored at the server, as opposed to a single file. This extends the scope of the authors’ past work that only considered the class of linear functions that operate element-wise over the files. On observing that the existing cache-aided scalar linear function retrieval scheme does not work in the proposed setting, this paper designs a novel coded caching scheme that outperforms uncoded caching schemes that either use unicast transmissions or let each user recover all files in the library.

On the Fundamental Limits of Coded Caching Systems With Restricted Demand Types

Caching is a technique to reduce the communication load in peak hours by prefetching contents during off-peak hours. An information theoretic framework for coded caching was introduced by Maddah-Ali and Niesen in a recent work, where it was shown that significant improvement can be obtained compared to uncoded caching. Considerable efforts have been devoted to identify the precise information theoretic fundamental limits of the coded caching systems, however the difficulty of this task has also become clear. One of the reasons for this difficulty is that the original coded caching setting allows all possible multiple demand types during delivery, which in fact introduces tension in the coding strategy. In this paper, we seek to develop a better understanding of the fundamental limits of coded caching by investigating systems with certain demand type restrictions. We first consider the canonical three-user three-file system, and show that, contrary to popular beliefs, the worst demand type is not the one in which all three files are requested. Motivated by these findings, we focus on coded caching systems where every file must be requested by at least one user. A novel coding scheme is proposed, which can provide new operating points that are not covered by any previously known schemes.

On Coded Caching With Private Demands

Caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the user’s local cache memory without knowledge of later demands. For the shared-link caching model, Maddah-Ali and Niesen (MAN) proposed a two-phase ( placement and delivery ) coded caching strategy, which is order optimal within a constant factor. However, in the MAN coded caching scheme, each user can obtain the information about the demands of other users, i.e., the MAN coded caching scheme is inherently prone to tampering and spying the activity/demands of other users. In this paper, we formulate an information-theoretic shared-link caching model with private demands, where there are ${\mathsf K}$ cache-aided users (which can cache up to ${\mathsf M}$ files) connected to a central server with access to ${\mathsf N}$ files. Each user requests ${\mathsf L}$ files. Our objective is to design a two-phase private caching scheme with minimum load while preserving the information-theoretic privacy of the demands of each user with respect to other users. A trivial solution is the uncoded caching scheme which lets each user recover all the ${\mathsf N}$ files, referred to as baseline scheme . For this problem we propose two novel schemes which achieve the information-theoretic privacy of the users’ demands while also achieving a non-trivial caching gain over the baseline scheme. The general underlying idea is to satisfy the users’ requests by generating a set of coded multicast messages that is symmetric with respect to the library files, such that for each user k, the mutual information between these messages and the demands of all other users given the cache content and the demand of user k is zero. In the first scheme, referred to as virtual-user scheme, we introduce a number of virtual users such that each ${\mathsf L}$ -subset of files is demanded by ${\mathsf K}$ real or virtual (effective) users and use the MAN delivery to generate multicast messages. From the viewpoint of each user, the set of multicast messages is symmetric over all files even if each single multicast message is not. This scheme incurs in an extremely large sub-packetization. Then, we propose a second scheme, referred to as MDS-based scheme, based on a novel MDS-coded cache placement. In this case, we generate multicast messages where each multicast message contains one MDS-coded symbol from each file in the library and thus is again symmetric over all the files from the viewpoint of each user. The sub-packetization level of the MDS-based scheme is exponentially smaller than that needed by the virtual-user scheme. Compared with the existing shared-link coded caching converse bounds without privacy, the virtual-user scheme is proved to be order optimal with a constant factor when ${\mathsf N}\leq {\mathsf L} {\mathsf K} $ , or when ${\mathsf N}\geq {\mathsf L} {\mathsf K} $ and ${\mathsf M}\geq {\mathsf N}/ {\mathsf K}$ . In addition, when ${\mathsf M}\geq {\mathsf N}/2$ , both of the virtual-user scheme and the MDS-based scheme are order optimal within a factor of 2.

Coded Caching in a Multi-Server System With Random Topology

Cache-aided content delivery is studied in a multi-server system with $P$ servers and $K$ users, each equipped with a local cache memory. In the delivery phase, each user connects randomly to any $\rho$ out of $P$ servers. Thanks to the availability of multiple servers, which model small-cell base stations (SBSs), demands can be satisfied with reduced storage capacity at each server and reduced delivery rate per server; however, this also leads to reduced multicasting opportunities compared to the single-server scenario. A joint storage and proactive caching scheme is proposed, which exploits coded storage across the servers, uncoded cache placement at the users, and coded delivery. The delivery \textit{latency} is studied for both \textit{successive} and \textit{parallel} transmissions from the servers. It is shown that, with successive transmissions the achievable average delivery latency is comparable to the one achieved in the single-server scenario, while the gap between the two depends on $\rho$, the available redundancy across the servers, and can be reduced by increasing the storage capacity at the SBSs. The optimality of the proposed scheme with uncoded cache placement and MDS-coded server storage is also proved for successive transmissions.

Fundamental Limits on the Regret of Online Network-Caching

Optimal caching of files in a content distribution network (CDN) is a problem of fundamental and growing commercial interest. Although many different caching algorithms are in use today, the fundamental performance limits of the network caching algorithms from an online learning point-of-view remain poorly understood to date. In this paper, we resolve this question in the following two settings: (1) a single user connected to a single cache, and (2) a set of users and a set of caches interconnected through a bipartite network. Recently, an online gradient-based coded caching policy was shown to enjoy sub-linear regret. However, due to the lack of known regret lower bounds, the question of the optimality of the proposed policy was left open. In this paper, we settle this question by deriving tight non-asymptotic regret lower bounds in the above settings. In addition to that, we propose a new Follow-the- Perturbed-Leader-based uncoded caching policy with near-optimal regret. Technically, the lower-bounds are obtained by relating the online caching problem to the classic probabilistic paradigm of balls-into-bins. Our proofs make extensive use of a new result on the expected load in the most populated half of the bins, which might also be of independent interest.We evaluate the performance of the caching policies by experimenting with the popular Movie- Lens dataset and conclude the paper with design recommendations and a list of open problems.

Fundamental Limits on the Regret of Online Network-Caching

Optimal caching of files in a content distribution network (CDN) is a problem of fundamental and growing commercial interest. Although many different caching algorithms are in use today, the fundamental performance limits of network caching algorithms from an online learning point-of-view remain poorly understood to date. In this paper, we resolve this question in the following two settings: (1) a single user connected to a single cache, and (2) a set of users and a set of caches interconnected through a bipartite network. Recently, an online gradient-based coded caching policy was shown to enjoy sub-linear regret. However, due to the lack of known regret lower bounds, the question of the optimality of the proposed policy was left open. In this paper, we settle this question by deriving tight non-asymptotic regret lower bounds in both of the above settings. In addition to that, we propose a new Follow-the-Perturbed-Leader-based uncoded caching policy with near-optimal regret. Technically, the lower-bounds are obtained by relating the online caching problem to the classic probabilistic paradigm of balls-into-bins. Our proofs make extensive use of a new result on the expected load in the most populated half of the bins, which might also be of independent interest. We evaluate the performance of the caching policies by experimenting with the popular MovieLens dataset and conclude the paper with design recommendations and a list of open problems.

On the Optimal Load-Memory Tradeoff of Cache-Aided Scalar Linear Function Retrieval

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.