Optimal Demand Private Coded Caching for Users with Small Buffers

This paper investigates the integration of coded caching (CC) into fluid antenna (FA) multiple access (FAMA) systems to overcome their fundamental performance limitations. While FAMA has demonstrated strong interference suppression capabilities without relying on precoding, its delivery rate saturates in the high signal-to-noise ratio (SNR) regime due to residual multi-user interference, and it requires at least as many transmit antennas as served users. On the other hand, CC eliminates multi-user interference by jointly designing caching and delivery phases, but suffers from the well-known worst-user bottleneck, especially under wireless fading channels and low SNR conditions. To overcome the interference-limited nature of FAMA and the worst-user bottleneck in CC, we consider a CC-enabled FAMA framework. The proposed approach enables interference-free transmission to multiple users using a single transmit antenna, and leverages adaptive port selection at the users to combat channel fading. We analyze the average rates and effective gains of XOR-based CC and the recently developed aggregated CC (ACC) schemes under the FAMA framework, and derive simple closed-form approximations that accurately characterize the performance. Furthermore, we rigorously prove that, in the limit where the number of FA ports grows without bound while maintaining sufficient spatial diversity, the effective multiplexing gains in the low-SNR limit of both XCC- and ACC-enabled FAMA asymptotically achieve the nominal gain that is only attainable under high-SNR conditions with traditional antennas. Simulation results show that the proposed architecture outperforms both conventional FAMA and traditional-antenna CC schemes, achieving significant spectral efficiency gains in a wide range of SNR regimes.

This paper studies device to device (D2D) coded-caching with information theoretic security guarantees. A broadcast network consisting of a server, which has a library of files, and end users equipped with cache memories, is considered. Information theoretic security guarantees for confidentiality are imposed upon the files. The server populates the end user caches, after which D2D communications enable the delivery of the requested files. Accordingly, we require that a user must not have access to files it did not request, i.e., secure caching. First, a centralized coded caching scheme is provided by jointly optimizing the cache placement and delivery policies. Next, a decentralized coded caching scheme is developed that does not require the knowledge of the number of active users during the caching phase. Both schemes utilize non-perfect secret sharing and one-time pad keying, to guarantee secure caching. Furthermore, the proposed schemes provide secure delivery as a side benefit, i.e., any external entity which overhears the transmitted signals during the delivery phase cannot obtain any information about the database files. The proposed schemes provide the achievable upper bound on the minimum delivery sum rate. Lower bounds on the required transmission sum rate are also derived using cut-set arguments indicating the multiplicative gap between the lower and upper bounds. Numerical results indicate that the gap vanishes with increasing memory size. Overall, the work demonstrates the effectiveness of D2D communications in cache-aided systems even when confidentiality constraints are imposed at the participating nodes and against external eavesdroppers.

Coded caching was introduced as a technique of systematically exploiting locally available storage at the clients to increase the channel throughput via coded transmissions. Most known coded caching schemes in literature enable large gains in terms of the rate, however at the cost of subpacketization that is exponential in $K^{\frac{1}{r}}$ ($K$ being the number of clients, $r$ some positive integer). Building upon recent prior work for coded caching design via line graphs and finite-field projective geometries, we present a new scheme in this work which achieves a subexponential (in $K$) subpacketization of $q^{O((\log_{q}{K})^2)}$ and rate $\Theta\left(\frac{K}{(\log_{q} {K})^2}\right)$, for large $K$, and the cached fraction $\frac{M}{N}$ being upper bounded by a constant $\frac{2}{q^{\alpha-1}}$ (for some prime power $q$ and constant $\alpha \geq 2$) . Apart from this asymptotic improvement, we show that through some numerical comparisons that our present scheme has much lower subpacketization than previous comparable schemes, however with an increased rate and some increase in cache size required. For instance, we obtain practically relevant subpacketization levels such as $10^2 - 10^7$ for $10^2 - 10^4$ number of clients. Leveraging prior results on adapting coded caching schemes for the error-free broadcast channel to device to device (D2D) networks, we obtain a low- subpacketization scheme for D2D networks also, and give numerical comparison for the same with prior work.

In the coded caching problem apart from transmission rate, reducing the number of packets $F$ ia also meaningful for practical implementation for coded caching scheme. Yan et al. reformulate the centralized coded caching schemes as designing a corresponding placement delivery array (PDA). In this letter, we propose two concatenating constructions by concatenating some known PDAs to obtain new PDAs therefore new code caching schemes with low sub-packetization level. Further, the comparison and analysis of parameters between our new schemes and known schemes is also performed.

The coded caching problem with shared caches where the server is equipped with multiple transmit antennas is considered. In a shared cache network, several users share a cache, but each user can access only a single cache. The fundamental limits of coded caching are known for the above setting under centralized uncoded placement. In the centralized case, to achieve the gains offered by coded caching, one requires a sub-packetization level which increases exponentially with the number of caches. The dedicated cache networks too had a similar issue, and placement delivery arrays (PDAs) were introduced as a solution to address the sub-packetization bottleneck of coded caching in the dedicated cache network. Our objective is to design coded caching schemes for shared caches with lower sub-packetization requirements than the existing schemes. By leveraging the PDA constructions, we propose a procedure to obtain new coded caching schemes for shared caches with reduced sub-packetization levels than the known schemes in both single and multi-antenna settings. The advantage of the proposed procedure is that all the existing PDA constructions can be transformed into coded caching schemes for shared caches, thereby reducing the sub-packetization level requirement. In addition, the proposed procedure also recovers the optimal caching schemes given by Parinello <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> by using a PDA corresponding to the Maddah-Ali Niesen scheme.

This work falls under the broad setting of coded caching with user-dependent file popularity and average-rate capacity analysis. In general, the exact capacity characterization with user-dependent file popularity remains an open problem. For example, user 1 may be interested in files 1 and 2 with probabilities 0.6 and 0.4, respectively, while user 2 may be interested in only files 2, and 3 with probabilities 1/3 and 2/3, respectively, but not interested in file 1 at all. An optimal scheme needs to carefully balance the conflicting interests under the given probabilistic weights. Motivated by this fundamental but intrinsically difficult problem, this work studies the following simplified setting: Each user k is associated with a file demand set (FDS) Θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ; each file in Θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> is equally desired by user k with probability 1/|Θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> | and files outside Θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> is not desired at all. Different users may have different Θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k1</sub> ≠ Θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k2</sub> , which reflects the user-dependent file popularity. Various capacity results have been derived (mostly for the cases of K = 2 users). One surprising byproduct is a proof showing that selfish coded caching is insufficient to achieve the capacity. That is, in an optimal coded caching scheme, a user sometimes has to cache the files of which he/she has zero interests.

Coded caching has received great attention as a promising method to alleviate the network traffic during peak-traffic times. Placement delivery array (PDA) was proposed to characterize the placement and delivery phases in a centralized coded caching system. In this paper, from the viewpoint of combinational design we construct a new class of PDA, and further reduce the subpacketization compared to the existing coded caching schemes by means of maximum distance separable (MDS) code.

In this paper, a centralized coded caching scheme is developed for wireless backhaul networks with heterogeneous channel conditions, i.e., the wireless channels between microBSs and a macroBS have different link rates and packet loss rates. To address these heterogeneous channel conditions, a joint random linear network coding and nested coded modulation (RLNCNCM) encoding scheme is designed for the delivery phase. Based on RLNC-NCM encoding, broadcast opportunities can be fully utilized for each coded subfile transmission. To support RLNC-NCM transmission, unequal file partition and cache size allocation are conducted in the placement phase. It is shown that a microBS with weaker channel condition needs to be allocated with more cache size. The theoretical achievable transmission time of the RLNC-NCM coded caching scheme is also derived. Moreover, numerical results show that the coded caching scheme developed in this paper significantly reduces the transmission time as compared to the existing schemes.

Coded caching can significantly decrease the communication load in peak hours of the network. The gain of caching is maximized in a centralized setting, where the cache content of users are opportunistically designed. In the absence of a centralized placement, users' caches are filled with randomly selected packets of the files. This yields to a loss in the caching gain, especially for small cache size. A novel placement scheme is introduced in this work which is based on (within file) precoding of the files at the server, followed by random cache placement. It is shown that the proposed technique improves the caching gain compared to the uncoded placement. Surprisingly, the performance of the proposed decentralized placement matches with that of the centralized placement for small cache size.

A coded caching scheme for efficient storage and access of medical data is discussed in this paper. Being an inspiring technology for improving the availability and sharing of medical data, the coded caching scheme for medical data is not only convenient for the medical staffs to grasp the patients’ health conditions and treatment history in time, but also effective for the patients to obtain improved quality of medical services. In this paper, the coded caching scheme for the combination network which is the model for the medical data sharing is studied. In the combination network, the server communicates with the users via multiple relays, and the relays as well as the users have cache memories. Using the maximum distance separable codes and placement delivery array (PDA) algorithm, the coded placement phase and delivery phase for combination networks are designed. In addition, for combination networks that satisfy the resolvability property, we extend the PDA algorithm to the case where the users’ priority is considered. The proposed scheme greatly reduces the subpacketization level with slightly increasing the transmission rate. The users with higher priority can get the requested content faster. We demonstrate that relays with cache memories can reduce the data transmission in peak time. The gap between the upper bound and lower bound of the transmission rate is gradually decreased with the increase in the users’ memories. The proposed scheme will shorten the latency time of the system and improve system efficiency for storage and access of medical data.

We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called cache) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. In this work, we propose a binary matrix model to construct the coded caching scheme. The ones in such a caching matrix indicate uncached subfiles at the users. Identity submatrices of the caching matrix represent transmissions in the delivery phase. Using this model, we then propose several novel constructions for coded caching based on the various types of combinatorial designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement (uncached fraction being Θ( √1K), K being the number of users), they provide a rate R that is upper bounded by a constant (R ≤ 1) with increasing K, and moreover require extremely small levels of subpacketization (being O(K)), which is an extremely important parameter in practical applications of coded caching.

In this survey paper, we review three recent main results on cache networks, which not only considerably sharpen the approximate characterization of the rate-memory trade off, but also extend those results to more general networks. In these systems, a server with a database of some files (e.g. movies) is connected to multiple users via a communication network. Each user has an isolated memory of limited size that can be used for caching. The system operates in two phases: a placement phase where users each store a portion of the files in their local cache, and a delivery phase, where the users each request a file and the server delivers coded messages to the users, fulfilling their file requests. We start by considering the shared bottleneck network in two flavors of the system, with uncoded prefetching and with coded prefetching. First, for uncoded prefetching, an optimal design is proposed, under both centralized and decentralized settings, for both peak rate and average rate. The exact optimality is proven through a matching converse. Second, for caching with coded prefetching, we present a design that is optimal within a factor of approximately 2, which strictly improves the state of the art. Lastly, we move the focus to more general network topologies, and present an order-wise optimal scheme that is independent of the underlying communication network between the server and the users. This scheme is shown to achieve the minimum delivery delay with a constant factor for all memoryless networks.

We study a multi-access variant of the popular coded caching framework, which consists of a central server with a catalog of $N$ files, $K$ caches with limited memory $M$, and $K$ users such that each user has access to $L$ consecutive caches with a cyclic wrap-around and requests one file from the central server's catalog. The server assists in file delivery by transmitting a message of size $R$ over a shared error-free link and the goal is to characterize the optimal rate-memory trade-off. This setup was studied previously by Hachem et al., where an achievable rate and an information-theoretic lower bound were derived. However, the multiplicative gap between them was shown to scale linearly with the access degree $L$ and thus order-optimality could not be established. A series of recent works have used a natural mapping of the coded caching problem to the well-known index coding problem to derive tighter characterizations of the optimal rate-memory trade-off under the additional assumption that the caches store uncoded content. We follow a similar strategy for the multi-access framework and provide new bounds for the optimal rate-memory trade-off $R^*(M)$ over all uncoded placement policies. In particular, we derive a new achievable rate for any $L \ge 1$ and a new lower bound, which works for any uncoded placement policy and $L \ge K/2$. We then establish that the (multiplicative) gap between the new achievable rate and the lower bound is at most $2$ independent of all parameters, thus establishing an order-optimal characterization of $R^*(M)$ for any $L\ge K/2$. This is a significant improvement over the previously known gap result, albeit under the restriction of uncoded placement policies. Finally, we also characterize $R^*(M)$ exactly for a few special cases.

The problem of $X$-secure $T$-private information retrieval from MDS coded storage is studied in this paper, where the user wishes to privately retrieve one out of $K$ independent messages that are distributed over $N$ servers according to an MDS code. It is guaranteed that any group of up to $X$ colluding servers learn nothing about the messages and that any group of up to $T$ colluding servers learn nothing about the identity of desired message. A lower bound of achievable rates is proved by presenting a novel scheme based on \emph{cross-subspace alignment} and a successive decoding with interference cancellation strategy. For large number of messages $(K\rightarrow\infty)$ the achieved rate, which we conjecture to be optimal, improves upon the best known rates previously reported in the literature by Raviv and Karpuk, and generalizes an achievable rate for MDS-TPIR previously found by Freij-Hollanti et al. that is also conjectured to be asymptotically optimal. The setting is then expanded to allow unresponsive and Byzantine servers. Finally, the scheme is applied to find a new lower convex hull of (download, upload) pairs of secure and private distributed matrix multiplication that generalizes, and in certain asymptotic settings strictly improves upon the best known previous results.

We consider a cache network, where a single server is connected to multiple users via a shared bottleneck link. The server has a set of files, which can be cached by each user in a prefetching phase. In a following delivery phase, each user requests a file and the server delivers user demands as efficiently as possible by taking into account their cache contents. We focus on an important and commonly used class of prefetching schemes, where the caches are filled with uncoded data. We provide the exact characterization of rate-memory tradeoff for this problem, by deriving both the minimum average rate (for a uniform file popularity) and the minimum peak rate required on the bottleneck link for a given cache size available at each user. We propose a novel caching scheme, which strictly improves the state of the art by exploiting commonality among user demands. We then demonstrate the exact optimality of our proposed scheme through a matching converse, by dividing the set of all demands into types, and showing that the placement phase in the proposed caching scheme is universally optimal for all types. Using these techniques, we can also fully characterize the rate-memory tradeoff for a decentralized setting, in which users fill out their cache content without coordination.