Low Subpacketization Coded Caching via Projective Geometry for Broadcast and D2D Networks

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.

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.

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.

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 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 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.

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.

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.

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.

Coded caching schemes on broadcast networks with user caches help to offload traffic from peak times to off-peak times by prefetching information from the server to the users during off-peak times and thus serving the users more efficiently during peak times using coded transmissions. We consider the problem of secretive coded caching which was proposed recently, in which a user should not be able to decode any information about any file that the user has not demanded. We propose a new secretive coded caching scheme which has a lower average rate compared to the existing state-of-the-art scheme, for the same memory available at the users. The proposed scheme is based on exploiting the presence of common demands between multiple users.

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.

Structural Properties of Models of N1-Categorical Theories

Deterministic estimator learning automata-based neighbor discovery schemes for D2D networks with directional antennas

Rill networks have been a focus of study for many decades, but we still lack a complete understanding of the variables that control the spacing of rills and the geometry of rill networks (e.g., parallel or dendritic) on hillslopes. In this paper, we investigate the controls on the spacing and geometry of rill networks using numerical modeling and comparison of the model results to terrestrial‐laser‐scanner‐derived topographic data from rill networks formed in physical experiments. The landscape evolution model accounts for the transport of sediment due to rain splash and fluvial entrainment as well as the deposition of sediment being advected by the overland flow. In order to develop realistic rill networks in the model, we find that it is necessary to incorporate the effects of raindrop impact within the fluvial sediment transport process. Model results are only consistent with those of experiments when raindrop‐aided fluvial sediment transport is accounted for. Dendritic networks are often predicted by the model in cases of high initial topographic roughness and high rates of advective (fluvial) sediment transport relative to diffusive (colluvial) transport. Parallel networks form within numerical experiments in low‐roughness cases under a wide range of relative advective and diffusive transport rates as well as in high roughness cases in which diffusive sediment transport is high relative to advective transport. The transition from dendritic to parallel rill networks is shown to occur gradually rather than being associated with a particular threshold. Finally, based on a balance between diffusive and advective sediment transport processes, we predict that the mean spacing between parallel rills scales with the square root of the ratio of diffusivity to channel erodibility.

Virtual local area networks (VLAN) is a well-known technology of computer security in heterogeneous network infrastructures. It does not require significant computing resources. For this reason, it should find success in Internet of things. The VLAN access control scheme formation is divided into the tasks of initial configuration and reconfiguration. The paper presents an approach to the reconfiguration of VLAN access control schemes based on the improved class of genetic algorithms. Unlike the initial configuration, the reconfiguration additionally uses the previous access control scheme as input. Its search criterion is focused on minimizing the possible changes in the previous scheme. The paper shows that this problem is a special form of the Boolean matrix factorization. Main enhancements relate to generation of the initial population based on trivial solutions, using the columns of the connectivity matrix as the genes of chromosomes and applying in the fitness function the criterion of minimal cost to modify the access scheme. Experimental results demonstrate the proposed genetic algorithm has a high enough effectiveness.