Placement Delivery Array Based on Concatenating Construction

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.

Coded caching is an effective technique to decongest the amount of traffic in the backhaul link. In such a scheme, each file hosted in the server is 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 with the number of packets. It is important to design a scheme with a small subpacketization level and a relatively low transmission rate. Recently, placement delivery array (PDA) was proposed to address the subpacketization bottleneck of coded caching. This paper investigates the design of PDA from a new perspective, i.e., the injective arc coloring of regular digraphs. It is shown that the injective arc coloring of a regular digraph can yield a PDA with the same number of rows and columns. Based on this, a new class of regular digraphs are defined and the upper bounds on the injective chromatic index of such digraphs are derived. Consequently, four new coded caching schemes with a linear subpacketization level and a relatively small transmission rate are proposed, one of which generalizes the existing scheme for the scenario with a more flexible number of users.

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.

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.

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.

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.

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. The existing secretive coded caching scheme for shared caches requires a subpacketization level, which is exponential in the number of helper caches. In this work, we propose a procedure to obtain new secretive coded caching schemes for shared caches with reduced subpacketization levels by utilizing the placement delivery array constructions. We also show that the existing secretive coded caching scheme for shared caches can be recovered using our procedure. In addition, a lower bound based on cut-set based arguments is derived for the shared cache networks under secrecy constraint and characterized the performance of the obtained scheme.

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 is an efficient technique to reduce peak-hour network traffic. One limitation of known coded caching schemes is that the demands of all users are revealed to their peers in the delivery phase. Schemes that assure privacy for user demands are studied in the recent past. Assuming that the users are equipped with caches of small memory sizes, the achievable rate under demand privacy constraints is investigated in this work. We present an MDS code based demand private coded caching scheme with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> users and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> files that achieves a memory rate pair <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\left(\frac{1}{K(N-1)+1}, N\, \left(1- \frac{1}{K(N-1)+1}\right)\right)$</tex> . The presented memory-rate pair meets the lower bound under demand-privacy requirements, proposed by Yan and Tuninetti in the recent work “Fundamental Limits of Caching for Demand Privacy against Colluding Users”. By memory sharing, the achievable memory-rate pair characterizes the exact rate-memory trade-off for the demand private coded caching scheme for cache memory <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M\in\left[0,\frac{1}{K(N-1)+1}\right]$</tex> .

The network load is increasing due to the spread of content distribution services. Caching is recognized as a technique to reduce a peak network load by prefetching popular contents into memories of users. Coded caching is a new caching approach based on a carefully designed content placement in order to create coded multicasting opportunities. Coded caching schemes in single-rate networks are evaluated by the trade-off between the size of memory and the size of delivered data. Considering the network with multiple transmission rates, it is important how to operate multicast. The multicast needs to use the smallest rate among the available rates for target users. In multi-rate wireless networks, multicast scheduling schemes are evaluated by a throughput and a delay. In this paper, we discuss coded caching in the multi- rate wireless networks. We newly define a throughput and a delay for evaluating the coded caching scheme and propose a new coded caching scheme suitable for these metrics. We compare the proposed coded caching scheme with conventional coded caching schemes.

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.

In a traditional (H,r) combination network, each user connects to a unique set of r relays. However, few research efforts have considered the (H,r,u) multiaccess combination network problem wherein each unique set of r relays is connected by u users. In this paper, we focus on designing coded caching schemes for a (H,r,u) multiaccess combination network. By directly applying the well-known coding method (proposed by Zewail and Yener) for a (H,r) combination network, a coded caching scheme (called ZY scheme) for (H,r,u) multiaccess combination network is obtained. However, its subpacketization has an exponential order with the number of users which leads to high implementation complexity. In order to reduce subpacketization, a direct construction of a coded caching scheme (called the direct scheme) for (H,r,u) multiaccess combination network is proposed by means of combinational design theory, where the parameter u must be a combinatorial number. For the arbitrary parameter u, the hybrid construction of a coded caching scheme (called the hybrid scheme) for the (H,r,u) multiaccess combination network is proposed based on the direct scheme. Theoretical and numerical analysis shows that the direct scheme and the hybrid scheme have a smaller transmission load for each relay compared with the naive scheme (which is obtained by repeatedly applying the coded caching scheme for a traditional (H,r) combination network by u times) and have much lower subpacketization compared with the ZY 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 is a promising solution to reduce the peak traffic in broadcast networks by prefetching the popular content close to end users and using coded transmissions. One of the chief issues of most coded caching schemes in literature is the issue of large subpacketization, i.e., they require each file to be divided into a large number of subfiles. In this work, we present a coded caching scheme using line graphs of bipartite graphs in conjunction with projective geometries over finite fields. The presented scheme achieves a rate Θ(K/log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> K) (K being the number of users, q is some prime power) with subexponential subpacketization q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O((logq K)^2)</sup> when cached fraction is upper bounded by a constant (M/N ≤ 1/q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> , for some positive integer α). Compared to earlier schemes, the presented scheme has a lower subpacketization (albeit possessing a higher rate). We also present a new subpacketization dependent lower bound on the rate for caching schemes in which each subfile is cached in the same number of users. Compared to the previously known bounds, this bound seems to perform better for a range of parameters of the caching system.

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.