Centralized coded caching schemes: A hypergraph theoretical approach

Shangguan, Chong; Zhang, Yiwei; Ge, Gennian

doi:10.48550/arxiv.1608.03989

Cited by 9 publications

(26 citation statements)

References 8 publications

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“…Let q, z and t be fixed and let m approximate infinity, it holds that R and M N are constants independent of K for all PDAs in Theorem 2. Similar to the discussion in [16], by means of the inequality (m/t) t < m t < (em/t) t , we can estimate the value of m by K, i.e., tK…”

Section: A Performance Analyses Of Theoremmentioning

confidence: 84%

“…From Table II, it is not difficult to check that our schemes have more flexible M N than that of the results in [16], [18], [24] and include all the results of [16], [24] listed in Table I as special cases. Because of the flexible memory size, our new schemes have the following two important advantages.…”

Section: Referencesmentioning

confidence: 99%

“…Then from the results in [16] and [18], we have two types of schemes directly, while according to the results in Table II, the following 14 schemes can be obtained. • For many values of M N , the schemes in Theorem 2 have both smaller F and R than those of the schemes generated by memory sharing based on [16] listed in Table I, and the schemes in Theorems 3 have both smaller F and R than those of the schemes generated by memory sharing based on [24] listed in Table I. The detailed discusses are proposed in Subsections III-A and III-B.…”

Section: Referencesmentioning

confidence: 99%

“…Furthermore, comparing with MN scheme they obtained two classes of coded caching schemes by means of constructing two infinite classes of PDAs such that F reduces significantly by increasing the rate very little. Inspired by the concept of a PDA, we construct some coded caching schemes with lower level subpacketization were proposed in [16], [18], [20], [24] from the view point of hypergraphs, resolvable combinatorial designs, Ruzsa-Szeméredi graphs, bipartite graphes respectively. For ease of exposition, the main previously known determined schemes are listed in Table I, which was summarised by Shangguang et al in [16].…”

Section: Introductionmentioning

confidence: 99%

“…Inspired by the concept of a PDA, we construct some coded caching schemes with lower level subpacketization were proposed in [16], [18], [20], [24] from the view point of hypergraphs, resolvable combinatorial designs, Ruzsa-Szeméredi graphs, bipartite graphes respectively. For ease of exposition, the main previously known determined schemes are listed in Table I, which was summarised by Shangguang et al in [16].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Constructions of Coded Caching Schemes With Flexible Memory Size

Cheng

Jiang

Yan

et al. 2019

IEEE Trans. Commun.

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Coded caching scheme recently has become quite popular in the wireless network due to its effectively reducing the transmission amount (denote such an amount by R) during peak traffic times. However to realize a coded caching scheme, each file must be divided into F packets which usually increases the computation complexity of a coded caching scheme. So we prefer to construct a caching scheme that decreases the order of F for practical implementations.In this paper, we construct four classes of new schemes where two classes can significantly reduce the value of F by increasing a little R comparing with the well known scheme proposed by Maddah-Ali and Niesen, and F in the other two classes grows sub-exponentially with K by sacrificing more R. It is worth noting that a tradeoff between R and F , which is a hot topic in the field of caching scheme, is proposed by our constructions. In addition, our constructions include all the results constructed by Yan et al., (IEEE Trans. Inf. Theory 63, 5821-5833, 2017) and some main results obtained by Shangguan et al., (arXiv preprint arXiv:1608.03989v1) as the special cases. Index TermsCoded caching scheme, placement delivery array, rate, packet number I. INTRODUCTIONRecently, the explosive increasing mobile services, especially applications such as video streaming, have imposed a tremendous pressure on the data transmission over the core network [1]. As a result, during the peak-traffic times, the communication systems are usually congested. Coded caching scheme, which was proposed by Maddah-Ali and Niesen in [12], can effectively reduce congestion during the peak-traffic times, and now is a hot topic in both industrial and academic fields (see [6]-[10], [12]-[14], [25], [28], and references therein).The benchmark work in [12] focused on the centralized caching system where a single server containing N files with the same length connects to K users over a shared link and each user has a cache memory of size M files. A coded caching scheme consists of two phases: a placement phase during off-peak times and a delivery phase during peak times. In the placement phase, the user caches are populated. This phase does not depend on the user demands which are assumed to be arbitrary. In delivery phase, each user requires a file from server. Then server sends a coded signal of at most R files to the users such that various user demands are satisfied with the help the local caches. It is meaningful to minimize the load R files in the delivery phase. Here R is always called the rate. A coded caching scheme is called F -division scheme if each file is split into F packets. If the packets of all files are directly cached in the placement phase, we call it uncoded placement. Otherwise we call it coded placement. Through an elaborate uncoded placement and a coded delivery, the first determined scheme for an F -division (K, M, N ) coded caching system with F = K KM/N , when KM N is an integer, was proposed by Maddah-Ali and Niesen in [12]. Such a scheme is referred to as MN scheme in this p...

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Section: A Performance Analyses Of Theoremmentioning

confidence: 84%

Section: Referencesmentioning

confidence: 99%

Section: Referencesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Constructions of Coded Caching Schemes With Flexible Memory Size

Cheng

Jiang

Yan

et al. 2019

IEEE Trans. Commun.

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Coded caching with linear subpacketization is possible using Ruzsa-Szeméredi graphs

Shanmugam¹,

Tulino

Dimakis

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Coded caching is a problem where encoded broadcasts are used to satisfy users requesting popular files and having caching capabilities. Recent work by Maddah-Ali and Niesen showed that it is possible to satisfy a scaling number of users with only a constant number of broadcast transmissions by exploiting coding and caching. Unfortunately, all previous schemes required the splitting of files into an exponential number of packets before the significant coding gains of caching appeared. The question of what can be achieved with polynomial subpacketization (in the number of users) has been a central open problem in this area. We resolve this problem and present the first coded caching scheme with polynomial (in fact, linear) subpacketization. We obtain a number of transmissions that is not constant, but can be any polynomial in the number of users with an exponent arbitrarily close to zero. Our central technical tool is a novel connection between Ruzsa-Szeméredi graphs and coded caching.

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Adding Transmitters Dramatically Boosts Coded-Caching Gains for Finite File Sizes

Lampiris

Elia

2018

IEEE J. Select. Areas Commun.

140

177

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In the context of coded caching in the K-user BC, our work reveals the surprising fact that having multiple (L) transmitting antennas, dramatically ameliorates the long-standing subpacketization bottleneck of coded caching by reducing the required subpacketization to approximately its Lth root, thus boosting the actual DoF by a multiplicative factor of up to L. In asymptotic terms, this reveals that as long as L scales with the theoretical caching gain, then the full cumulative (multiplexing + full caching) gains are achieved with constant subpacketization. This is the first time, in any known setting, that unbounded caching gains appear under finite file-size constraints. The achieved caching gains here are up to L times higher than any caching gains previously experienced in any single-or multiantenna fully-connected setting, thus offering a multiplicative mitigation to a subpacketization problem that was previously known to hard-bound caching gains to small constants.The proposed scheme is practical and it works for all values of K, L and all cache sizes. The scheme's gains show in practice: e.g. for K = 100, when L = 1 the theoretical caching gain of G = 10, under the original coded caching algorithm, would have needed subpacketization S 1 = K G = 100 10 > 10 13 , while if extra transmitting antennas were added, the subpacketization was previously known to match or exceed S 1 . Now for L = 5, our scheme offers the theoretical (unconstrained) cumulative DoF d L = L + G = 5 + 10 = 15, with subpacketization S L = K/L G/L = 100/5 10/5 = 190. The work extends to the multi-server and cache-aided IC settings, while the scheme's performance, given subpacketization S L = K/L G/L , is within a factor of 2 from the optimal linear sum-DoF.

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Centralized coded caching schemes: A hypergraph theoretical approach

Cited by 9 publications

References 8 publications

Constructions of Coded Caching Schemes With Flexible Memory Size

Constructions of Coded Caching Schemes With Flexible Memory Size

Coded caching with linear subpacketization is possible using Ruzsa-Szeméredi graphs

Adding Transmitters Dramatically Boosts Coded-Caching Gains for Finite File Sizes

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