The idea of coded caching was introduced by Maddah-Ali and Niesen who demonstrated the advantages of coding in caching problems. To capture the essence of the problem, they introduced the $(N, K)$ canonical cache network in which $K$ users with independent caches of size $M$ request files from a server that has $N$ files. Among other results, the caching scheme and lower bounds proposed by them led to a characterization of the exact rate memory tradeoff when $M\geq \frac{N}{K}(K-1)$. These lower bounds along with the caching scheme proposed by Chen et al. led to a characterization of the exact rate memory tradeoff when $M\leq \frac{1}{K}$. In this paper we focus on small caches where $M\in \left[0,\frac{N}{K}\right]$ and derive new lower bounds. For the case when $\big\lceil\frac{K+1}{2}\big\rceil\leq N \leq K$ and $M\in \big[\frac{1}{K},\frac{N}{K(N-1)}\big]$, our lower bounds demonstrate that the caching scheme introduced by G{ó}mez-Vilardeb{ó} is optimal and thus extend the characterization of the exact rate memory tradeoff. For the case $1\leq N\leq \big\lceil\frac{K+1}{2}\big\rceil$, we show that the new lower bounds improve upon the previously known lower bounds.
In this work, we study coded placement in caching systems where the users have unequal cache sizes and demonstrate its performance advantage. In particular, we propose a caching scheme with coded placement for three-user systems that outperforms the best caching scheme with uncoded placement. In our proposed scheme, users cache both uncoded and coded pieces of the files, and the coded pieces at the users with large memories are decoded using the unicast/multicast signals intended to serve users with smaller memories. Furthermore, we extend the proposed scheme to larger systems and show the red…
This paper considers the secretive coded caching problem with shared caches in which no user must have access to the files that it did not demand. In a shared cache network, the users are served by a smaller number of helper caches and each user is connected to exactly one helper cache. To ensure the secrecy constraint in shared cache networks, each user is required to have an individual cache of at least unit file size. For this setting, a secretive coded caching scheme was proposed recently in the literature (\enquote{Secretive Coded Caching with Shared Caches}, in \textit{IEEE Communication…
We consider the coded caching problem with shared caches where several users share a cache, but each user has access to only a single cache. For this network, the fundamental limits of coded caching are known for centralized and decentralized settings under uncoded placement. In the centralized case, to achieve the gains offered by coded caching, one requires a sub-packetization which increases exponentially with the number of caches. The dedicated cache networks had a similar issue, and placement delivery arrays (PDAs) were introduced as a solution to it. Using the PDA framework, we propose a…
The work identifies the fundamental limits of coded caching when the K receiving users share Λ$\leq$ K helper-caches, each assisting an arbitrary number of different users. The main result is the derivation of the exact optimal worst-case delivery time - under the assumption of uncoded cache placement - for any user-to-cache association profile, where each such profile describes how many users are helped by each cache. This is achieved with a new information-theoretic converse that is based on index coding and which proves that a simple XOR-shrinking-and-removal coded-caching scheme is optimal…
We consider the problem of \emph{secretive coded caching} in a shared cache setup where the number of users accessing a particular \emph{helper cache} is more than one, and every user can access exactly one helper cache. In secretive coded caching, the constraint of \emph{perfect secrecy} must be satisfied. It requires that the users should not gain, either from their caches or from the transmissions, any information about the content of the files that they did not request from the server. In order to accommodate the secrecy constraint, our problem setup requires, in addition to a helper cache…
This work explores coded caching in the symmetric $K$-user cache-aided MISO BC with imperfect CSIT-type feedback, for the specific case where the cache size is much smaller than the library size. Building on the recently explored synergy between caching and delayed-CSIT, and building on the tradeoff between caching and CSIT quality, the work proposes new schemes that boost the impact of small caches, focusing on the case where the cumulative cache size is smaller than the library size. For this small-cache setting, based on the proposed near-optimal schemes, the work identifies the optimal cac…
This work considers the coded caching problem with shared caches, where users share the caches, and each user gets access only to one cache. The user-to-cache association is assumed to be known at the server during the placement phase. We focus on the schemes derived using placement delivery arrays (PDAs). The PDAs were originally designed to address the sub-packetization bottleneck of coded caching in a dedicated cache setup. We observe that in the setup of this paper permuting the columns of the PDA results in schemes with different performance for the same problem, but the sub-packetization…
Building on the recent coded-caching breakthrough by Maddah-Ali and Niesen, the work here considers the $K$-user cache-aided wireless multi-antenna (MISO) symmetric broadcast channel (BC) with random fading and imperfect feedback, and analyzes the throughput performance as a function of feedback statistics and cache size. In this setting, our work identifies the optimal cache-aided degrees-of-freedom (DoF) within a factor of 4, by identifying near-optimal schemes that exploit the new synergy between coded caching and delayed CSIT, as well as by exploiting the unexplored interplay between cachi…
Within the context of coded caching, the work reveals the interesting connection between having multiple transmitters and having heterogeneity in the cache sizes of the receivers. Our work effectively shows that having multiple transmit antennas -- while providing full multiplexing gains -- can also simultaneously completely remove the performance penalties that are typically associated to cache-size unevenness. Focusing on the multiple-input single-output Broadcast Channel, the work first identifies the performance limits of the extreme case where cache-aided users coincide with users that do…
Recently Hachem et al. formulated a multiaccess coded caching model which consists of a central server connected to $K$ users via an error-free shared link, and $K$ cache-nodes. Each cache-node is equipped with a local cache and each user can access $L$ neighbouring cache-nodes with a cyclic wrap-around fashion. In this paper, we take the privacy of the users' demands into consideration, i.e., each user can only get its required file and can not get any information about the demands of other users. By storing some private keys at the cache-nodes, we propose a novel transformation approach to t…
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 \emph{at most three file groups} in the optimal cache placement{, where files within a group have the same cache placement}. We furthe…
This paper investigates the fundamental tradeoff between cache size and download time in the (H;r;M;N) combination network, where a server with N files is connected to H relays (without caches) and each of the K:=\binom{H}{r} users (with caches of size M files) is connected to a different subset of r relays. Existing schemes fall within two categories: either use the uncoded symmetric cache placement originally proposed for the shared-link model and design delivery phase dependent on the network topology, or effectively divide the combination network into H independent shared-link networks eac…
Coded caching schemes with low subpacketization and small transmission rate are desirable in practice due to the requirement of low implementation complexity and efficiency of the transmission. Placement delivery arrays (PDA in short) can be used to generate coded caching schemes. However, many known coded caching schemes have large memory ratios. In this paper, we realize that some schemes with low subpacketization generated by PDAs do not fully use the users' caching content to create multicasting opportunities and thus propose to overcome this drawback. As an application, we obtain two new …
The tradeoff between the user's memory size and the worst-case download time in the $(H,r,M,N)$ combination network is studied, where a central server communicates with $K$ users through $H$ immediate relays, and each user has local cache of size $M$ files and is connected to a different subset of $r$ relays. The main contribution of this paper is the design of a coded caching scheme with asymmetric coded placement by leveraging coordination among the relays, which was not exploited in past work. Mathematical analysis and numerical results show that the proposed schemes outperform existing sch…
A centralized coded caching system, consisting of a server delivering N popular files, each of size F bits, to K users through an error-free shared link, is considered. It is assumed that each user is equipped with a local cache memory with capacity MF bits, and contents can be proactively cached into these caches over a low traffic period; however, without the knowledge of the user demands. During the peak traffic period each user requests a single file from the server. The goal is to minimize the number of bits delivered by the server over the shared link, known as the delivery rate, over al…
This paper considers a cache-aided device-to-device (D2D) system where the users are equipped with cache memories of different size. During low traffic hours, a server places content in the users' cache memories, knowing that the files requested by the users during peak traffic hours will have to be delivered by D2D transmissions only. The worst-case D2D delivery load is minimized by jointly designing the uncoded cache placement and linear coded D2D delivery. Next, a novel lower bound on the D2D delivery load with uncoded placement is proposed and used in explicitly characterizing the minimum …
Decentralized coded caching is studied for a content server with $N$ files, each of size $F$ bits, serving $K$ active users, each equipped with a cache of distinct capacity. It is assumed that the users' caches are filled in advance during the off-peak traffic period without the knowledge of the number of active users, their identities, or the particular demands. User demands are revealed during the peak traffic period, and are served simultaneously through an error-free shared link. A new decentralized coded caching scheme is proposed for this scenario, and it is shown to improve upon the sta…
Coded caching is an information theoretic scheme to reduce high peak hours traffic by partially prefetching files in the users local storage during low peak hours. This paper considers heterogeneous decentralized caching systems where cache of users and content library files may have distinct sizes. The server communicates with the users through a Gaussian broadcast channel. The main contribution of this paper is a novel modulation strategy to map the multicast messages generated in the coded caching delivery phase to the symbols of a signal constellation, such that users can leverage their ca…
Classical coded caching setting avails each user to have one dedicated cache. This is generalized to a more general shared cache scheme and the exact expression for the worst case rate was derived in [E. Parrinello, A. Unsal, P. Elia, "Fundamental Limits of Caching in Heterogeneous Networks with Uncoded Prefetching," available on arXiv:1811.06247 [cs.IT], Nov. 2018]. For this case, an optimal linear error correcting delivery scheme is proposed and an expression for the peak rate is established for the same. Furthermore, a new delivery scheme is proposed, which gives an improved rate for the ca…
The combination of edge caching and coded multicasting is a promising approach to improve the efficiency of content delivery over cache-aided networks. The global caching gain resulting from content overlap distributed across the network in current solutions is limited due to the increasingly personalized nature of the content consumed by users. In this paper, the cache-aided coded multicast problem is generalized to account for the correlation among the network content by formulating a source compression problem with distributed side information. A correlation-aware achievable scheme is propo…
Decentralized coded caching scheme, introduced by Maddah-Ali and Niesen, assumes that the caches are filled with no coordination. This work identifies a decentralized coded caching scheme -- under the assumption of uncoded placement -- for shared cache network, where each cache serves multiple users. Each user has access to only a single cache and the number of caches is less than or equal to the number of users. For this setting, we derive the optimal worst-case delivery time for any user-to-cache association profile where each such profile describes the number of users served by each cache. …
Coded caching is an emerging technique to reduce the data transmission load during the peak-traffic times. In such a scheme, each file in the data center or library is usually divided into a number of packets to pursue a low broadcasting rate based on the designed placements at each user's cache. However, the implementation complexity of this scheme increases as the number of packets increases. It is crucial to design a scheme with a small subpacketization level, while maintaining a relatively low transmission rate. It is known that the design of caches in users (i.e., the placement phase) and…
Network based on distributed caching of content is a new architecture to alleviate the ongoing explosive demands for rate of multi-media traffic. In caching networks, coded caching is a recently proposed technique that achieves significant performance gains compared to uncoded caching schemes. In this paper, we derive a lower bound on the average rate with a memory constraint for a family of caching allocation placement and a family of XOR cooperative delivery. The lower bound inspires us how placement and delivery affect the rate memory tradeoff. Based on the clues, we design a new placement …
In this paper, we study shared cache coded caching (SC-CC): a set of caches serves a larger set of users; each user access one cache, and a cache may serve many users. For this problem, under uncoded placement, Parrinello, Ünsal, and Elia showed an optimal SC-CC scheme, in which the subpacketization level depends upon the number of caches. We show an SC-CC scheme where the subpacketization level does not directly depend upon the number of users or caches; any number of caches and users can be accommodated for a fixed subpacketization level. Furthermore, new caches can be added without re-doing…
We consider distributed and dynamic caching of coded content at small base stations (SBSs) in an area served by a macro base station (MBS). Specifically, content is encoded using a maximum distance separable code and cached according to a time-to-live (TTL) cache eviction policy, which allows coded packets to be removed from the caches at periodic times. Mobile users requesting a particular content download coded packets from SBSs within communication range. If additional packets are required to decode the file, these are downloaded from the MBS. We formulate an optimization problem that is ef…
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 $…
We consider a centralized caching network, where a server serves several groups of users, each having a common shared homogeneous fixed-size cache and requesting arbitrary multiple files. An existing coded prefetching scheme is employed where each file is broken into multiple fragments and each cache stores multiple coded packets each formed by XORing fragments from different files. For such a system, we propose an efficient file delivery scheme with explicit constructions by the server to meet the arbitrary multi-requests of all user-groups. Specifically, the stored coded packets of each cach…
In this work, we consider a slight variant of well known coded caching problem, referred as multi-access coded caching problem, where each user has access to $z$ neighboring caches in a cyclic wrap-around way. We present a placement and delivery scheme for this problem, under the restriction of uncoded placement. Our work is a generalization of one of the cases considered in "Multi-access coded caching : gains beyond cache-redundancy" by B. Serbetci, E. Parrinello and P. Elia. To be precise, when our scheme is specialized to $z=\frac{K-1}{K γ}$, for any $K γ$, where $K$ is the number of users …
Caching is an efficient way to reduce peak-hour network traffic congestion by storing some contents at user's local cache without knowledge of later demands. Maddah-Ali and Niesen initiated a fundamental study of caching systems; they proposed a scheme (with uncoded cache placement and linear network coding delivery) that is provably optimal to within a factor 12. In this paper, by noticing that when the cache contents and the demands are fixed, the caching problem can be seen as an index coding problem, we show the optimality of Maddah-Ali and Niesen's scheme assuming that cache placement is …
The well known Maddah-Ali-Niesen (MAN) coded caching scheme for users with dedicated cache is extended for use in multi-access coded cache scheme where the number of users need not be same as the number of caches in the system. The well known MAN scheme is recoverable as a special case of the multi-access system considered. The performance of this scheme is compared with the existing works on multi-access coded caching. To be able to compare the performance of different multi-access schemes with different number of users for the same number of caches, the terminology of per user rate (rate div…
Motivated by applications to delivery of dynamically updated, but correlated data in settings such as content distribution networks, and distributed file sharing systems, we study a single source multiple destination network coded multicast problem in a cache-aided network. We focus on models where the caches are primarily located near the destinations, and where the source has no cache. The source observes a sequence of correlated frames, and is expected to do frame-by-frame encoding with no access to prior frames. We present a novel scheme that shows how the caches can be advantageously used…
In this paper, we aim to minimize the average file transmission delay via bandwidth allocation and cache placement in two-tier heterogeneous networks with limited storage capacity, which consists of cache capacity and buffer capacity. For average delay minimization problem with fixed bandwidth allocation, although this problem is nonconvex, the optimal solution is obtained in closed form by comparing all locally optimal solutions calculated from solving the Karush-Kuhn-Tucker conditions. To jointly optimize bandwidth allocation and cache placement, the optimal bandwidth allocation is first der…
Decentralized proactive caching and coded delivery is studied in a content delivery network, where each user is equipped with a cache memory, not necessarily of equal capacity. Cache memories are filled in advance during the off-peak traffic period in a decentralized manner, i.e., without the knowledge of the number of active users, their identities, or their particular demands. User demands are revealed during the peak traffic period, and are served simultaneously through an error-free shared link. The goal is to find the minimum delivery rate during the peak traffic period that is sufficient…
We consider content caching between a service provider and multiple cache-enabled users, using the recently proposed modified coded caching scheme (MCCS) that provides an improved delivery strategy for random user requests. We develop the optimal cache placement solution for the MCCS with arbitrary cache size by formulating the cache placement as an optimization problem to minimize the average rate during the delivery phase under random user requests. Through reformulation, we show that the problem is a linear programming problem. By exploring the properties in the caching constraints, we obta…
We study the problem of multi-access coded caching (MACC): a central server has $N$ files, $K$ ($K \leq N$) caches each of which stores $M$ out of the $N$ files, $K$ users each of which demands one out of the $N$ files, and each user accesses $z$ caches. The objective is to jointly design the placement, delivery, and user-to-cache association, to optimize the achievable rate. This problem has been extensively studied in the literature under the assumption that a user accesses only one cache. However, when a user accesses more caches, this problem has been studied only under the assumption that…
Coded caching scheme provides us an effective framework to realize additional coded multicasting gain by exploiting coding into multiple transmitted signals. The goal of coded caching design is to jointly optimize the placement and delivery scheme so as to minimize the amount of transmitted coded signals. However, few research efforts consider multiple-round coded caching design problem, in which fixed and mobile users may coexist in one network different number of active users present in successive rounds. Obviously, such dynamic network configurations may lead to undesired frequent placement…
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. Motivated …
Centralized coded caching problem is studied for the two-user scenario, considering heterogeneous cache capacities at the users and private channels from the server to the users, in addition to a shared channel. Optimal caching and delivery strategies that minimize the worst-case delivery latency are presented for an arbitrary number of files. The converse proof follows from the sufficiency of file-index-symmetric caching and delivery codes, while the achievability is obtained through memory-sharing among a number of special memory capacity pairs. The optimal scheme is shown to exploit the pri…
We consider a cache-aided wireless device-to-device (D2D) network of the type introduced by Ji, Caire, and Molisch [1], where the placement phase is orchestrated by a central server. We assume that the devices' caches are filled with uncoded data, and the whole content database is contained in the collection of caches. After the cache placement phase, the files requested by the users are serviced by inter-device multicast communication. For such a system setting, we provide the exact characterization of the optimal load-memory trade-off under the assumptions of uncoded placement and one-shot d…
The coded caching scheme is an efficient technique as a solution to reduce the wireless network burden during the peak times in a Device-to-Device (D2D in short) communications. In a coded caching scheme, each file block should be divided into $F$ packets. It is meaningful to design a coded caching scheme with the rate and $F$ as small as possible, especially in the practice for D2D network. In this paper we first characterize coded caching scheme for D2D network by a simple array called D2D placement delivery array (DPDA in shot). Consequently some coded caching scheme for D2D network can be …
This paper considers heterogeneous coded caching where the users have unequal distortion requirements. The server is connected to the users via an error-free multicast link and designs the users' cache sizes subject to a total memory budget. In particular, in the placement phase, the server jointly designs the users' cache sizes and the cache contents. To serve the users' requests, in the delivery phase, the server transmits signals that satisfy the users' distortion requirements. An optimization problem with the objective of minimizing the worst-case delivery load subject to the total cache m…
This work considers the multi-access caching system proposed by Hachem et al., where each user has access to L neighboring caches in a cyclic wrap-around fashion. We first propose a placement strategy called the consecutive cyclic placement, which achieves the maximal local caching gain. Then under the consecutive cyclic placement, we derive the optimal coded caching gain from the perspective of Placement Delivery Array (PDA), thus obtaining a lower bound on the rate of PDA. Finally, under the consecutive cyclic placement, we construct a class of PDA, leading to a multi-access coded caching sc…
The idea of coded caching for content distribution networks was introduced by Maddah-Ali and Niesen, who considered the canonical $(N, K)$ cache network in which a server with $N$ files satisfy the demands of $K$ users (equipped with independent caches of size $M$ each). Among other results, their work provided a characterization of the exact rate memory tradeoff for the problem when $M\geq\frac{N}{K}(K-1)$. In this paper, we improve this result for large caches with $M\geq \frac{N}{K}(K-2)$. For the case $\big\lceil\frac{K+1}{2}\big\rceil\leq N \leq K$, we propose a new coded caching scheme, …
Coded caching technique is an efficient approach to reduce the transmission load in networks and has been studied in heterogeneous network settings in recent years. In this paper, we consider a new widespread caching system called $(K_1,K_2,U,r,M,N)$ two-dimensional (2D) caching-aided ultra-dense network (UDN) with a server containing $N$ files, $K_1K_2$ cache nodes arranged neatly on a grid with $K_1$ rows and $K_2$ columns, and $U$ cache-less users randomly distributed around cache nodes. Each cache node can cache at most $M\leq N$ files and has a certain service region by Euclidean distance…
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 cache…
This paper introduces the notion of cache-tapping into the information theoretic models of coded caching. The wiretap channel II in the presence of multiple receivers equipped with fixed-size cache memories, and an adversary which selects symbols to tap into from cache placement and/or delivery is introduced. The legitimate terminals know neither whether placement, delivery, or both are tapped, nor the positions in which they are tapped. Only the size of the overall tapped set is known. For two receivers and two files, the strong secrecy capacity -- the maximum achievable file rate while keepi…
We consider a cache network in which a single server is connected to multiple users via a shared error free link. The server has access to a database with $N$ files of equal length $F$, and serves $K$ users each with a cache memory of $MF$ bits. A novel centralized coded caching scheme is proposed for scenarios with more users than files $N\leq K$ and cache capacities satisfying $\frac{1}{K}\leq M\leq\frac{N}{K}$. The proposed scheme outperforms the best rate-memory region known in the literature if $N\leq K\leq\frac{N^{2}+1}{2}$.
Li {\it et al}. introduced coded distributed computing (CDC) scheme to reduce the communication load in general distributed computing frameworks such as MapReduce. They also proposed cascaded CDC schemes where each output function is computed multiple times, and proved that such schemes achieved the fundamental trade-off between computation load and communication load. However, these schemes require exponentially large numbers of input files and output functions when the number of computing nodes gets large. In this paper, by using the structure of placement delivery arrays (PDAs), we construc…
