Coded Caching based on Combinatorial Designs

Agrawal, Shailja; Sree, K V Sushena; Krishnan, Prasad

doi:10.48550/arxiv.1901.06383

Cited by 3 publications

(5 citation statements)

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Section: Appendixmentioning

confidence: 99%

“…In addition to this using Y m , the m th user gets the subfile indices shown in the sequence of expressions numbered (11) to (17). Notice that the last expression in (17) is the union of all the blocks in a parallel class. So from the property of resolvable designs the above set is equal to the set containing all the subfile indices of all the files and therefore it also contains all the subfiles of the demanded file W dm .…”

Section: Appendixmentioning

confidence: 99%

“…Various combinatorial designs have been used in different setups of coded caching [14], [16], [17]. To the best of our knowledge this is the first work that uses designs for multiaccess coding caching.…”

Section: Introductionmentioning

confidence: 99%

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Multi-access Coded Caching Schemes From Cross Resolvable Designs

Katyal¹,

M²,

Rajan³

2020

Preprint

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We present a novel caching and coded delivery scheme for a multi-access network where multiple users can have access to the same cache (shared cache) and any cache can assist multiple users. This scheme is obtained from resolvable designs satisfying certain conditions which we call cross resolvable designs. To be able to compare different multi-access coded schemes with different number of users we normalize the rate of the schemes by the number of users served. Based on this per-user-rate we show that our scheme performs better than the well known Maddah-Ali -Nieson (MaN) scheme and the recently proposed ("Multi-access coded caching : gains beyond cache-redundancy" by Serbetci, Parrinello and Elia) SPE scheme. It is shown that the resolvable designs from affine planes are cross resolvable designs and our scheme based on these performs better than the MaN scheme for large memory size cases. The exact size beyond which our performance is better is also presented. The SPE scheme considers only the cases where the product of the number of users and the normalized cache size is 2, whereas the proposed scheme allows different choices depending on the choice of the cross resolvable design.

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Section: Appendixmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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Multi-access Coded Caching Schemes From Cross Resolvable Designs

Katyal¹,

M²,

Rajan³

2020

Preprint

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“…The problem of designing a coded caching scheme thus becomes that of designing the appropriate PDA for some given parameters. Although the schemes proposed by Yan et al in [11] have significantly lower complexity than that of the Ali-Niesen schemes (i.e., the value of F is smaller) [6] at the cost of a slight increase in rate, F still increases exponentially with K. Several new methods for constructing PDAs have since been reported, see for example [1], [2], [9], [5], [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Placement Delivery Arrays from Combinations of Strong Edge Colorings

Michel

Wang

2019

2019 Ninth International Workshop on Signal Design and Its Applications in Communications (IWSDA)

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It has recently been pointed out in both of the works [C. Shanguan, Y. Zhang, and G. Ge, IEEE Trans. Inform. Theory, 64(8):5755-5766 (2018)] and [Q. Yan, X. Tang, Q. Chen, and M. Cheng, IEEE Commun. Lett., 22(2):236-239 (2018)] that placement delivery arrays (PDAs), as coined in [Q. Yan, M. Cheng, X. Tang, and Q. Chen, IEEE Trans. Inform. Theory, 63(9):5821-5833 (2017)], are equivalent to strong edge colorings of bipartite graphs. In this paper we consider various methods of combining two or more edge colorings of bipartite graphs to obtain new ones, and therefore new PDAs. We find that combining PDAs in certain ways also gives a framework for obtaining PDAs with more robust and flexible parameters. We investigate how the parameters of certain strong edge colorings change after being combined with others, and we compare the parameters of the resulting PDAs with those of known ones.

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“…In order to find subfile indices that m th user get from all (b r − 1) z transmissions, we have to vary the value of e s such that e s = a s , ∀s ∈[z].The m th user is able to receive subfile indices given bybr es = 1, es = as ∀s ∈ [z] {C 1,e1 ∩ C 2,e2 ∩ • • • ∩ C z,ez }.In addition to this using Y m , the m th user gets the subfile indices shown in the sequence of expressions numbered (14) to (20), as shown at the top of the page 13. Notice that the last expression in(17) is the union of all the blocks in a parallel class. So from the property of resolvable designs the above set is equal to the set∩ t∈X \m Y t = ls = {is,js}, ∀s ∈ [z] (l1,l2,...,lz) = (a1,a2,...,az) {C 1,l1 ∪ C 2,l2 ∪ • • • ∪ C z,lz } ls = {is,js}, ∀s ∈ [2,z] {C 1,e1 ∪ C 2,l2 ∪ • • • ∪ C z,lz } ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ls = {is,js}, ∀s ∈ [2,z] (l2,l3,...,lz) = (a2,a3,...,az) {C 1,a1 ∪ C 2,l2 ∪ • • • ∪ C z,lz } ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ = C 1,e1 ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ls = {is,js}, ∀s ∈ [2,z] (l2,l3,...,lz) = (a2,a3,...,az) {C 1,a1 ∪ C 2,l2 ∪ C 3,l3 ∪ • • • ∪ C z,lz } ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ls = {is,js},∀s ∈ [2,z] (l2,l3,...,lz) = (a2,a3,...,az)…”

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confidence: 99%

Multi-Access Coded Caching Schemes From Cross Resolvable Designs

Katyal

Muralidhar

Rajan

2021

IEEE Trans. Commun.

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We present a novel caching and coded delivery scheme for a multi-access network where multiple users can have access to the same cache (shared cache) and multiple caches can be accessed by the same user. This scheme is obtained from resolvable designs satisfying certain conditions which we call cross resolvable designs. To be able to compare different multi-access coded schemes with different number of users we normalize the rate of the schemes by the number of users served. Based on this per-user-rate we show that our scheme performs better than the well known Maddah-Ali -Niesen (MaN) scheme and the recently proposed ("Multi-access coded caching: gains beyond cache-redundancy" by Serbetci, Parrinello and Elia) SPE scheme. It is shown that the resolvable designs from affine planes are cross resolvable designs and our scheme based on these performs better than the MaN scheme for large memory size cases. The exact size beyond which our performance is better is also presented. The SPE scheme considers only the cases where the product of the number of users and the normalized cache size is 2, whereas the proposed scheme allows different choices depending on the choice of the cross resolvable design.

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Coded Caching based on Combinatorial Designs

Cited by 3 publications

References 0 publications

Multi-access Coded Caching Schemes From Cross Resolvable Designs

Multi-access Coded Caching Schemes From Cross Resolvable Designs

Placement Delivery Arrays from Combinations of Strong Edge Colorings

Multi-Access Coded Caching Schemes From Cross Resolvable Designs

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