Global Cache Research Articles

A hybrid Bi-level management framework for caching and communication in Edge-AI enabled IoT

The proliferation of IoT devices has led to a surge in network traffic, resulting in higher energy usage and response delays. In-network caching has emerged as a viable solution to address this issue. However, caching IoT data faces two key challenges: the transient nature of IoT content and the unknown spatiotemporal content popularity. Additionally, the use of a global view on dynamic IoT networks is problematic due to the high communication overhead involved. To tackle these challenges, this paper presents an adaptive management approach that jointly optimizes caching and communication in IoT networks using a novel bi-level control method called BC3. The approach employs two types of controllers: a global ILP-based optimal controller for long-term timeslots and local learning-based controllers for short-term timeslots. The long-term controller periodically establishes a global cache policy for the network and sends specific cache rules to each edge server. The local controller at each edge server solves the joint problem of bandwidth allocation and cache adaptation using deep reinforcement learning (DRL) technique. The main objective is to minimize energy consumption and system response time with utilizing the global and local observations. Experimental results demonstrate that the proposed approach increases cache hit rate by approximately 12% and uses 11% less energy compared to the other methods. Increasing the cache hit rate can lead to a reduction in about 17% in response time for user requests. Our bi-level control approach offers a promising solution for leveraging the network's global visibility while balancing communication overhead (as energy consumption) against system performance. Additionally, the proposed method has the lowest cache eviction, around 19% lower than the lowest eviction of the other comparison methods. The eviction metric is a metric to evaluate the effectiveness of adaptive caching approach designed for transient data.

Coalgebraic Satisfiability Checking for Arithmetic $\mu$-Calculi

The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus includes an exponential-time upper bound on satisfiability checking, which however relies on the availability of tableau rules for the next-step modalities that are sufficiently well-behaved in a formally defined sense; in particular, rule matches need to be representable by polynomial-sized codes, and the sequent duals of the rules need to absorb cut. While such rule sets have been identified for some important cases, they are not known to exist in all cases of interest, in particular ones involving either integer weights as in the graded $\mu$-calculus, or real-valued weights in combination with non-linear arithmetic. In the present work, we prove the same upper complexity bound under more general assumptions, specifically regarding the complexity of the (much simpler) satisfiability problem for the underlying one-step logic, roughly described as the nesting-free next-step fragment of the logic. The bound is realized by a generic global caching algorithm that supports on-the-fly satisfiability checking. Notably, our approach directly accommodates unguarded formulae, and thus avoids use of the guardedness transformation. Example applications include new exponential-time upper bounds for satisfiability checking in an extension of the graded $\mu$-calculus with polynomial inequalities (including positive Presburger arithmetic), as well as an extension of the (two-valued) probabilistic $\mu$-calculus with polynomial inequalities.

Multi-Antenna Coded Caching for Location-Dependent Content Delivery

Human-computer interaction continuously evolves towards a genuinely immersive experience, submerging users in a three-dimensional (3D) virtual world. A realistic, immersive experience necessitates a highly reliable and agile wireless connection to support immense data transmission. Yet, there are abundant but underutilized memory resources available at the devices which can be harnessed as supplementary assets to reduce the excessive burden on the wireless medium. What is more, the use of Coded Caching (CC) techniques enables the cumulative cache memory of users in the network to be used as an additional communication resource. To this end, a location-dependent multi-antenna CC-based content delivery scheme tailored specifically for wireless extended reality applications is proposed in this paper. First, a novel memory allocation process is developed, enabling an appropriate trade-off between local and global caching gains. In this regard, the local caching gain is maximized when the memory is mostly dedicated to locations with poor connectivity conditions (absolute fairness). In contrast, the global caching gain is maximized when the memory is uniformly allocated among all the locations. As a result of the memory allocation process, unequal fractions of location-dependent multimedia content are cached by each user. Given the asymmetric cache placement, a novel algorithm is proposed to create suitable codewords for each user during the subsequent delivery phase, which simultaneously achieves a global and local caching gain. The proposed delivery scheme also combines global caching and spatial multiplexing gains using a weighted max-min multicast beamformer design with multi-rate modulation. Numerical experiments and mathematical analysis demonstrate significant performance gains, in terms of the 95-percentile expected delivery time, compared to unicast and multicast scenarios where either the local or global caching gain is maximized.

UAV Assisted Cooperative Caching on Network Edge Using Multi-Agent Actor-Critic Reinforcement Learning

In recent times, caching at edge nodes is a well-known technique to overcome the limitation of strict latency, which simultaneously improves users' Quality of Experience (QoE). However, choosing an appropriate caching policy and content placement poses another significant issue that has been acknowledged in this research. Conventional caching policies that are experimented with at the edge do not consider the dynamic and stochastic characteristics of edge caching. As a result, we have proposed a cooperative deep reinforcement learning algorithm that deals with the dynamic nature of content demand. It also ensures efficient use of storage through the cooperation between nodes. In addition, previous works on cooperative caching have assumed the users to be static and didn't consider the mobile nature of users. Therefore, we have proposed UAVs as aerial Base Stations (UAV-BS) to assist in peak hours where a ground base station is insufficient to support the surge in user requests. In this novel research, we have demonstrated the cooperation between aerial and Ground Base Stations (GBS) and aimed at maximizing the global cache hit ratio. Simulations have shown that our proposed Cooperative Multi-Agent Actor-Critic algorithm outperforms conventional and reinforcement learning based caching methods and achieves a state-of-the-art global cache hit ratio when there is a surge in user requests. Thus, it opens the door for further research on cooperative caching in joint air and ground architecture.

Cache-Aided Matrix Multiplication Retrieval

Coded caching is a promising technique to smooth out network traffic by storing part of the library content at the users’ local caches. The seminal work on coded caching for single file retrieval by Maddah-Ali and Niesen (MAN) showed the existence of a global caching gain that scales with the total memory in the system, in addition to the known local caching gain in uncoded systems. This paper formulates a novel cache-aided matrix multiplication retrieval problem, relevant for data analytics and machine learning applications. In the considered problem, each cache-aided user requests the product of two matrices from the library. A structure-agnostic solution is to treat each possible matrix product as an independent file and use the MAN coded caching scheme for single file retrieval. This paper proposes two structure-aware schemes, which partition each matrix in the library by either rows or columns and let a subset of users cache some sub-matrices, that improve on the structure-agnostic scheme. For the case where the library matrices are “fat” matrices, the structure-aware row-partition scheme is shown to be order optimal under some constraint.

Stream Processing of Shortest Path Query in Dynamic Road Networks

Shortest path query in road network is pervasive in various location-based services nowadays. As the business expands, the scalability issue becomes severer and more servers are deployed to cope with it. Moreover, as the traffic condition keeps changing over time, the existing index-based approaches can hardly adapt to the real-life dynamic environment. Therefore, batch shortest path algorithms have been proposed recently to answer a set of queries together using shareable computation. Besides, they can also work in a highly dynamic environment as no index is needed. However, the existing batch algorithms either assume the batch queries are finely decomposed or just process them without differentiation, resulting in poor query efficiency. In this work, we assume the traffic condition is stable over a short period and treat the issued queries within that period as a stream of query sets. Specifically, we first propose three query set decomposition methods to cluster one query set into multiple query subsets: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Zigzag</i> that considers the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-N</i> shared computation; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Co-Clustering</i> that considers the source and target's spatial locality; and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Search-Space-Aware</i> that further incorporates search space estimation. After that, we propose two batch algorithms that take advantage of the previously decomposed query sets for efficient query answering: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R2R</i> that finds a set of approximate shortest paths from one region to another with bounded error; and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Local Cache</i> that improves the existing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Global Cache</i> with higher cache hit ratio. Finally, we design three efficient stream processing methods for intra-batch shared computation. The experiments on a large real-world query sets verify the effectiveness and efficiency of our decomposition methods compared with the state-of-the-art batch algorithms.

Low-Complexity High-Performance Cyclic Caching for Large MISO Systems

Multi-antenna coded caching is known to combine a global caching gain that is proportional to the cumulative cache size found across the network, with an additional spatial multiplexing gain that stems from using multiple transmitting antennas. However, a closer look reveals two severe bottlenecks; the well-known exponential subpacketization bottleneck that dramatically reduces performance when the communicated file sizes are finite, and the considerable optimization complexity of beamforming multicast messages when the SNR is finite. We here present an entirely novel caching scheme, termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cyclic multi-antenna</i> coded caching, whose unique structure allows for the resolution of the above bottlenecks in the crucial regime of many transmit antennas. For this regime, where the multiplexing gain can exceed the coding gain, our new algorithm is the first to achieve the exact one-shot linear optimal DoF with a subpacketization complexity that scales only linearly with the number of users, and the first to benefit from a multicasting structure that allows for exploiting uplink-downlink duality in order to yield optimized beamformers ultra-fast. In the end, our novel solution provides excellent performance for networks with finite SNR, finite file sizes, and many users.

Coalgebraic Reasoning with Global Assumptions in Arithmetic Modal Logics

We establish a generic upper bound ExpTime for reasoning with global assumptions (also known as TBoxes) in coalgebraic modal logics. Unlike earlier results of this kind, our bound does not require a tractable set of tableau rules for the instance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that potentially avoids building the entire exponential-sized space of candidate states, and thus offers a basis for practical reasoning. This algorithm still involves frequent fixpoint computations; we show how these can be handled efficiently in a concrete algorithm modelled on Liu and Smolka’s linear-time fixpoint algorithm. Finally, we show that the upper complexity bound is preserved under adding nominals to the logic, i.e., in coalgebraic hybrid logic.

Research on the Overview of Image Processing Architecture of Computer Based Deep Neural Network Accelerator

DNN algorithm still has many shortcomings in the process of operation, which need to be further solved. Specifically, there is more data reuse, and the repeated access of global cache takes up more resources and computation, thus reducing the efficiency of operation. Based on this, this paper first analyses the research status and value of the DNN accelerator, then studies the image processing architecture of the DNN accelerator, and finally gives the computer DNN model and acceleration algorithm analysis.

An FPGA‐Based Convolutional Neural Network Coprocessor

In this paper, an FPGA‐based convolutional neural network coprocessor is proposed. The coprocessor has a 1D convolutional computation unit PE in row stationary (RS) streaming mode and a 3D convolutional computation unit PE chain in pulsating array structure. The coprocessor can flexibly control the number of PE array openings according to the number of output channels of the convolutional layer. In this paper, we design a storage system with multilevel cache, and the global cache uses multiple broadcasts to distribute data to local caches and propose an image segmentation method that is compatible with the hardware architecture. The proposed coprocessor implements the convolutional and pooling layers of the VGG16 neural network model, in which the activation value, weight value, and bias value are quantized using 16‐bit fixed‐point quantization, with a peak computational performance of 316.0 GOP/s and an average computational performance of 62.54 GOP/s at a clock frequency of 200 MHz and a power consumption of about 9.25 W.

Improving performance of a distributed file system using hierarchical collaborative global caching algorithm with rank-based replacement technique

Improving performance of a distributed file system using hierarchical collaborative global caching algorithm with rank-based replacement technique

Joint Content-Mobility Priority Modeling for Cached Content Selection in D2D Networks

One key component for efficient opportunistic device-to-device (D2D) deployment is cache management. It determines which content to store opportunistic D2D communications. Existing solutions focus on the nature of content or mobility attributes, but most of them neglect their joint influence. Moreover, most solutions rely on a preloading phase, filling caches with content that the respective users may not consume, but that may be of interest to other nodes, and increasing traffic overhead in the core network. Further, a popular file may be a lousy candidate for opportunistic D2D because contact opportunities may not provide enough transfer capacity. To solve this issue, we propose a model that computes priority values based on both content and mobility attributes. Our approach considers only files that users have consumed, therefore eliminating a preloading phase. Using real-world and synthetic mobility traces, we compare our solution with Least Recently Stored replacement, as well as a state-of-the-art approach that also considers content and mobility attributes. Results show an increase in the global cache hit rate of almost 80% in scenarios that offer many files, and of around 420% in scenarios with a few users. The priority model generates 90% lower overhead in terms of the control bytes. We also apply our solution in a chunk-based adaptive video streaming application. We observe that our solution leads to higher video delivery ratios when compared to the baselines.

Improving Performance of a Distributed File System using Hierarchical Collaborative Global Caching Algorithm with Rank-Based Replacement Technique

In the emerging big data scenario, distributed file systems play a vital role for storage and access of large data generated in the web-based information systems. Improving performance of a distributed file system is a very important research issue in the current context. Client side caching and prefetching techniques enhance performance of the distributed file system. Efficient replacement policy is required to improve performance of the caching process. In this paper, we have proposed a novel client side caching algorithm namely hierarchical collaborative global caching algorithm and a cache replacement algorithm namely rank-based cache replacement algorithm. We have used support value computed for the file blocks, for prefetching, caching and replacement purposes. We have proved through simulation experiments that the proposed algorithm performs better than the existing algorithms discussed in the literature.

Adaptive Coded Caching for Fair Delivery Over Fading Channels

The performance of existing coded caching schemes is sensitive to the worst channel quality, a problem which is exacerbated when communicating over fading channels. In this paper, we address this limitation in the following manner: in short-term, we allow transmissions to subsets of users with good channel quality, avoiding users with fades, while in long-term we ensure fairness among users. Our online scheme combines (i) the classical decentralized coded caching scheme with (ii) joint scheduling and power control for the fading broadcast channel, as well as (iii) congestion control for ensuring the optimal long-term average performance. We prove that our online delivery scheme maximizes the alpha-fair utility among all schemes restricted to decentralized placement. By tuning the value of alpha, the proposed scheme can achieve different operating points on the average delivery rate region and tune performance according to an operator's choice. We demonstrate via simulations that our scheme outperforms two baseline schemes: (a) standard coded caching with multicast transmission, limited by the worst channel user yet exploiting the global caching gain; (b) opportunistic scheduling with unicast transmissions exploiting the fading diversity but limited to local caching gain.

The imaginary futures of Arabic: Egyptian dystopias in translation

ABSTRACT The growing phenomenon of novels using ʿammiyya (Arabic dialects) has reignited debates on the impact of local language on the regional and global trajectories of Arabic literature. While there is a long history of novelists using dialect for dialogues alongside fuṣḥā (Modern Standard Arabic, henceforth MSA), increasingly elements of ʿammiyya are incorporated throughout. This trend has been a feature of recent Egyptian novels which have been translated and marketed under the global cache of the dystopia label. While the source texts strategically evoke ʿammiyya and MSA, in translation a tension emerges between the familiarity of the dystopia genre and an effort to reclaim a linguistic spectrum for literary Arabic. Examining how translators negotiate local languages in Egyptian dystopian novels reveals the parameters that shape the production, translation and reception of Arabic literature today.

Optimizing Access to Memory Pages in Software-Implemented Global Page Cache Systems

This paper is based on a dissertation “Techniques for organizing shared access to distributed memory pages in cloud computing systems” defended at the Igor Sikorsky Kyiv Polytechnic Institute in 2017. The paper describes distributed page processing in Oracle Real Application Clusters (Oracle RAC) and compares it with other well-known processing methods. The comparison includes analysis of different architectures (including shared nothing, shared disk, and replication-based architectures) in terms of SQL query processing and asserts the soundness of the distributed page approach (also known as global cache fusion) to cloud database management systems (DBMSs). As a result of analyzing the global cache fusion approach, the main drawback of Oracle RAC systems—increasing queue problem—is revealed; it causes the impossibility to process queries once their rate exceeds a certain threshold inversely proportional to the packet delivery time between nodes. To eliminate the increasing queue problem when accessing distributed pages, a new access method is proposed that introduces an additional page state—unloading state—which improves the efficiency of distributed page processing by reducing the number of transfers between nodes during hot page processing. In addition to cloud DBMSs, the proposed method can also be used in other cloud systems with page-organized distributed memory architecture.

Prisons and picnics: tough talk and accent in Australian TV drama

Reflecting on the current TV landscape dominated by global streaming, Fremantle’s Jo Porter suggests that Australian TV is currently riding a high, with ‘quality’ dramas ‘cutting through’ and ‘getting noticed’ internationally. For Porter, this level of global visibility is occurring despite the barrier of its regional or ‘accented’ voice. However, in this article, I suggest that the global cache of certain Australian dramas may in fact be the product of accented storytelling rather than something to be conquered or overcome. In shaping this argument, I consider language politics and accent shifts in Australian TV history particularly in relation to exporting, format trade and remaking, exploring links between Grundy Television and Fremantle. By comparing language and accent in the cult classic Prisoner with Fremantle’s Wentworth and Picnic at Hanging Rock, I consider how the inclusion and exclusion of vernacular voice sheds light on industrial change and TV history.

Benefits of Cache Assignment on Degraded Broadcast Channels

Degraded K-user broadcast channels (BCs) are studied when the receivers are facilitated with cache memories. Lower and upper bounds are derived on the capacity-memory tradeoff, i.e., on the largest rate of reliable communication over the BC as a function of the receivers’ cache sizes, and the bounds are shown to match for interesting special cases. The lower bounds are achieved by two new coding schemes that benefit from nonuniform cache assignments . Lower and upper bounds are also established on the global capacity-memory tradeoff, i.e., on the largest capacity-memory tradeoff that can be attained by optimizing the receivers’ cache sizes subject to a total cache memory budget. The bounds coincide when the total cache memory budget is sufficiently small or sufficiently large, where the thresholds depend on the BC statistics. For small cache memories, it is optimal to assign all the cache memory to the weakest receiver. In this regime, the global capacity-memory tradeoff grows by the total cache memory budget divided by the number of files in the system. In other words, a perfect global caching gain is achievable in this regime and the performance corresponds to a system where all the cache contents in the network are available to all receivers. For large cache memories, it is optimal to assign a positive cache memory to every receiver, such that the weaker receivers are assigned larger cache memories compared to the stronger receivers. In this regime, the growth rate of the global capacity-memory tradeoff is further divided by the number of users, which corresponds to a local caching gain. It is observed numerically that a uniform assignment of the total cache memory is suboptimal in all regimes, unless the BC is completely symmetric. For erasure BCs, this claim is proved analytically in the regime of small cache sizes.

Increasing network throughput based on dynamic caching policy at wireless access points

The explosive growth of wireless data traffic not only challenges the design and evolution of the wireless network architecture, but also brings profound impacts on the quality of service and the quality of experience. As an appealing way to solve the low capacity of user equipment and high latency of network connection, wireless edge caching has attracted great attention of academia and industry recently. In wireless edge caching, popular content can be cached in the base stations or wireless access points (APs) or other devices closer to users. By taking advantage of this feature, devices in wireless edge caching are able to cache popular content that may be duplicated requested and still maintain the quality of services they shall provide. Therefore, with aim to minimum the content fetching delay and increase network throughput in the wireless network, we lucubrated the wireless edge caching in this paper. Firstly, we built a classical wireless APs caching model, then jointly considered the size and popularity of content and introduced an objective function, evaluating the content popularity on this basis to guarantee the global cache hit rate. Moreover, we used 0–1 knapsack problem dynamic programming to maximize the local cache hit rate of wireless AP. Finally, we statistically analyzed on real data traces to find some significant discoveries and analyzed the performance of 0–1 knapsack dynamic programming.

Cooperative Caching in Two-Layer Hierarchical Cache-aided Systems

Caching has received much attention as a promising technique to overcome high data rate and stringent latency requirements in the future wireless networks. The premise of caching technique is to prefetch most popular contents closer to end users in local cache of edge nodes, e.g., base station (BS). When a user requests a content that is available in the cache, it can be served directly without being sent from the core network. In this paper, we investigate the performance of hierarchical caching systems, in which both BS and end users are equipped with a storage memory. In particular, we propose a novel cooperative caching scheme that jointly optimizes the content placement at the BS’s and users’ caches. The proposed caching scheme is analytically shown to achieve a larger global caching gain than the reference in both uncoded – and coded caching strategies. Finally, numerical results are presented to demonstrate the effectiveness of our proposed caching algorithm.&#x0D; Keywords&#x0D; Hierarchical caching system, cooperative caching, caching gain, uncoded caching, coded caching&#x0D; References&#x0D; [1] D. Liu, B. Chen, C. Yang, A.F. Molisch, Caching at the Wireless Edge: Design Aspects, Challenges, and Future Directions, IEEE Communications Magazine 54 (2016) 22-28. https://doi.org/10.1109/MCOM.2016.7565183.[2] T.X. Vu, S. Chatzinotas, B. Ottersten, Edge-Caching Wireless Networks: Performance Analysis and Optimization, IEEE Transactions on Wireless Communications 17 (2018) 2827-2839. https://doi.org/10.1109/TWC.2018.2803816.[3] M.A. Maddah-Ali, U. Niesen, Fundamental Limits of Caching, IEEE Transactions on Information Theory 60 (2014) 2856-2867. https://doi.org/10.1109/TIT.2014.2306938.[4] M.A. Maddah-Ali, U. Niesen, Decentralized Coded Caching Attains Order-Optimal Memory-Rate Tradeoff, IEEE/ACM Transactions on Networking 23 (2015) 1029-1040. https://doi.org/10.1109/TNET.2014.2317316.[5] U. Niesen, M.A. Maddah-Ali, Coded Caching with Nonuniform Demands, IEEE Transactions on Information Theory 63 (2017) 1146-1158. https://doi.org/10.1109/TIT.2016.2639522.[6] Q. Yu, M.A. Maddah-Ali, A.S. Avestimehr, The exact rate-memory tradeoff for caching with uncoded prefetching, IEEE Transactions on Information Theory 64 (2018) 1281-1296. https://doi.org/10.1109/TIT.2017.2785237.[7] S.P. Shariatpanahi, H. Shah-Mansouri, B.H. Khalaj, Caching gain in interference-limited wireless networks, IET Communications 9 (2015) 1269-1277. https://doi.org/10.1049/iet-com.2014.0955.[8] N. Naderializadeh, M.A. Maddah-Ali, A.S. Avestimehr, Fundamental limits of cache-aided interference management, IEEE Transactions on Information Theory 63 (2017) 3092-3107. https://doi.org/10.1109/TIT.2017.2669942.[9] J. Hachem, U. Niesen, S. Diggavi, Energy-Efficiency Gains of Caching for Interference Channels, IEEE Communications Letters 22 (2018) 1434-1437. https://doi.org/10.1109/LCOMM.2018.2822694.[10] M.A. Maddah-Ali, U. Niesen, Cache-aided interference channels, IEEE International Symposium on Information Theory ISIT, 2015, pp. 809-813. https://doi.org/10.1109/ISIT.2015.7282567.[11] T.X. Vu, S. Chatzinotas, B. Ottersten, T.Q. Duong, Energy minimization for cache-assisted content delivery networks with wireless backhaul, IEEE Wireless Communications Letters 7 (2018) 332-335. https://doi.org/10.1109/LWC.2017.2776924.[12] S. Li, Q. Yu, M.A. Maddah-Ali, A.S. Avestimehr, Coded distributed computing: Fundamental limits and practical challenges, 50th Asilomar Conference on Signals, Systems and Computers (2016) 509-513. https://doi.org/ 10.1109/ACSSC.2016.7869092.[13] S. Li, M.A. Maddah-Ali, Q. Yu, A.S. Avestimehr, A fundamental tradeoff between computation and communication in distributed computing, IEEE Transactions on Information Theory 64 (2018) 109-128. https://doi.org/10.1109/TIT.2017.2756959.[14] S. Borst, V. Gupta, A. Walid, Distributed caching algorithms for content distribution networks, Proceedings IEEE INFOCOM. (2010) 1-9. https://doi.org/10.1109/INFCOM.2010.5461964.[15] N. Karamchandani, U. Niesen, M.A. Maddah-Ali, SN Diggavi, Hierarchical coded caching, IEEE Transactions on Information Theory 62 (2016) 3212-3229. https://doi.org/10.1109/TIT.2016.2557804.[16] S.P. Shariatpanahi, G. Caire, B. H. Khalaj, Multi-antenna coded caching, IEEE International Symposium on Information Theory ISIT, 2017, pp. 2113-2117. https://doi.org/10.1109/ISIT.2017.8006902.[17] R. Pedarsani, M.A. Maddah-Ali, U. Niesen, Online coded caching, IEEE/ACM Transactions on Networking 24 (2016) 836-845. https://doi.org/10.1109/TNET.2015.2394482.