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Coded Caching with Linear Subpacketization is Possible using Ruzsa-Szeméredi Graphs [article]

Karthikeyan Shanmugam, Antonia M. Tulino, Alexandros G. Dimakis
2017 arXiv   pre-print
Our central technical tool is a novel connection between Ruzsa-Szem\'eredi graphs and coded caching.  ...  We resolve this problem and present the first coded caching scheme with polynomial (in fact, linear) subpacketization.  ...  Ruzsa-Szeméredi Graphs and Coded Caching We start with the definition of Ruzsa-Szeméredi Graphs and establish the connection to the centralized coded caching problem.  ... 
arXiv:1701.07115v1 fatcat:zzgkbyqjvnhvrjn3v36cqqz4bq

From Centralized to Decentralized Coded Caching [article]

Yitao Chen, Karthikeyan Shanmugam, Alexandros G. Dimakis
2018 arXiv   pre-print
R ≤ K (1-M/N)/g transmissions, each file has to be divided into number of subpackets that is exponential in g.  ...  We consider the problem of designing decentralized schemes for coded caching. In this problem there are K users each caching M files out of a library of N total files.  ...  With a given (K, M, N, F ) Ruzsa-Szemerédi bipartite graph G([F ], [K], E), an F -packet coded caching scheme can be realized by Algorithm 1.  ... 
arXiv:1801.07734v1 fatcat:6sqpi7nlzzdafjma2qamchu75u

A Multi-Antenna Coded Caching Scheme with Linear Subpacketization [article]

MohammadJavad Salehi, Antti Tölli, Seyed Pooya Shariatpanahi
2019 arXiv   pre-print
Exponentially growing subpacketization is known to be a major issue for practical implementation of coded caching, specially in networks with multi-antenna communication setups.  ...  We provide a new coded caching scheme for such networks, which requires linear subpacketization and is applicable to any set of network parameters, as long as the multi-antenna gain L is larger than or  ...  In [20] Ruzsa-Szeméredi graphs are used to design coded caching schemes with linear subpacketization as K → ∞, but with non-constant R * . C.  ... 
arXiv:1910.10384v2 fatcat:bba35x32vnhjpohx7w7geqngai

Improving Placement Delivery Array Coded Caching Schemes with Coded Placement

Mingming Zhang, Minquan Cheng, Jinyu Wang, Xi Zhong, Yishan Chen
2020 IEEE Access  
However, many known coded caching schemes, which have low subpacketizations, realized by PDAs do not fully use the users' caching content to create multicasting opportunities.  ...  Coded caching schemes with low subpacketization and small transmission rate are desirable in practice due to the requirement of low implementation complexity and efficiency of transmission.  ...  design and linear block codes [14] , the (r, t) Ruzsa-Szeméredi graphs [7] , [13] , the strong edge coloring of bipartite graphs [9] , projective space [16] , etc.  ... 
doi:10.1109/access.2020.3042849 fatcat:egzeaizcdfbmbi2s5bprq3u35q

Diagonal Multi-Antenna Coded Caching for Reduced Subpacketization

MohammadJavad Salehi, Antti Tolli
2020 GLOBECOM 2020 - 2020 IEEE Global Communications Conference  
Large subpacketization requirement is known to be a significant issue in the practical implementation of multiantenna coded caching schemes.  ...  We find the lower-bound for the required subpacketization for any DCC scheme and show that it is achievable using simple, novel algorithms.  ...  In [17] , Ruzsa-Szeméredi graphs are used to design CC schemes with linear subpacketization growth, but with non-constant rate. C.  ... 
doi:10.1109/globecom42002.2020.9348098 fatcat:fmus7snsmzgbvhdhr45senuk6y

Design of Coded Caching Schemes with Linear Subpacketizations Based on Injective Arc Coloring of Regular Digraphs [article]

Xianzhang Wu, Minquan Cheng, Li Chen, Congduan Li, Zifan Shi
2022 arXiv   pre-print
Consequently, some new coded caching schemes with a linear subpacketization level and a small transmission rate are proposed, one of which generalizes the existing scheme for the scenario with a more flexible  ...  Coded caching is an effective technique to decongest the amount of traffic in the backhaul link.  ...  Apart from PDA, other coded caching schemes with a reduced subpacketization level were designed by the use of Ruzsa-Szemerédi graphs [13] , projective geometry and line graphs [10] , hypergraphs [12  ... 
arXiv:2207.09690v1 fatcat:jxtnlvf2jbbxxl36bb7qxp3nfu

Lifting Constructions of PDAs for Coded Caching with Linear Subpacketization [article]

V R Aravind, Pradeep Kiran Sarvepalli, Andrew Thangaraj
2022 arXiv   pre-print
In contrast, placement and delivery schemes in coded caching, designed using placement delivery arrays (PDAs), can have linear subpacketization with a penalty in rate.  ...  A crucial parameter in coded caching is subpacketization, which is the number of parts a file is to be split into for coding purposes.  ...  All authors are with the Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036, India. Email: {ee13d205, pradeep, andrew}@ee.iitm.ac.in  ... 
arXiv:2007.07475v2 fatcat:xiiz26cbxfchrdp5ue2yxkezty

Coded Caching Schemes with Linear Subpacketizations [article]

Xi Zhong, Minquan Cheng, Ruizhong Wei
2020 arXiv   pre-print
As an application, two classes of coded caching schemes with linear subpacketizations and small transmission rates are obtained.  ...  In coded caching system we prefer to design a coded caching scheme with low subpacketization and small transmission rate (i.e., the low implementation complexity and the efficient transmission during the  ...  Apart from PDA, there are many other characterizations of coded caching schemes such as hypergraphs [18] , strong edge coloring of bipartite graphs [21] , Ruzsa-Szeméredi graphs [17] , combinatorial  ... 
arXiv:2005.06126v3 fatcat:pig5urqsbffmpeqib5uiylz2ve

Coded Caching with Polynomial Subpacketization [article]

Wentu Song, Kui Cai, Long Shi
2020 arXiv   pre-print
We construct a family of centralized coded caching schemes with polynomial subpacketization.  ...  The server has a database of N files with each file being divided into F packets (F is known as subpacketization), and each user owns a local cache that can store M/N fraction of the N files.  ...  More interestingly, a family of coded caching schemes with linear subpacketization (i.e., F = K), were constructed in [17] , using the Ruzsa-Szeméredi graphs.  ... 
arXiv:2001.07020v1 fatcat:eichrx5bpnhwhb7djgnfnkuncy

Subexponential and Linear Subpacketization Coded Caching via Line Graphs and Projective Geometry [article]

Hari Hara Suthan Chittoor, Prasad Krishnan, K V Sushena Sree, Bhavana MVN
2020 arXiv   pre-print
In this work, we propose a new framework known as caching line graphs for centralized coded caching and utilize projective geometries over finite fields to construct two new coded caching schemes with  ...  Large gains in the rate of cache-aided broadcast communication are obtained using coded caching, but to obtain this most existing centralized coded caching schemes require that the files at the server  ...  The asymptotic nature of subpacketization with large K and constant cache fraction M N are shown wherever possible.  ... 
arXiv:2001.00399v1 fatcat:tcvqd7mrczfbfhl22xpglg6ojq

Adding transmitters dramatically boosts coded-caching gains for finite file sizes [article]

Eleftherios Lampiris, Petros Elia
2018 arXiv   pre-print
The work extends to the multi-server and cache-aided IC settings, while the scheme's performance, given subpacketization S_L=K/LG/L, is within a factor of 2 from the optimal linear sum-DoF.  ...  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.  ...  The authors are with the Communication Systems Department at EURECOM, Sophia Antipolis, 06410, France (email: lam-piris@eurecom.fr, elia@eurecom.fr).  ... 
arXiv:1802.03389v1 fatcat:xgq3sy5hojfmlcgpyemcqpcq5y

A framework of constructing placement delivery arrays for centralized coded caching [article]

Minquan Cheng, Jinyu Wang, Xi Zhong, Qiang Wang
2021 arXiv   pre-print
In caching system, it is desirable to design a coded caching scheme with the transmission load R and subpacketization F as small as possible, in order to improve efficiency of transmission in the peak  ...  Yan et al. reformulated the centralized coded caching scheme as designing a corresponding F× K array called placement delivery array (PDA), where F is the subpacketization and K is the number of users.  ...  , 3)-free hypergraphs [16] , the (r, t) Ruzsa-Szeméredi graphs [17] , the strong edge coloring of bipartite graphs [18] , the projective space over F p [19] , combinatorial design [20] and so on.  ... 
arXiv:1908.05865v3 fatcat:wudizy2oencvllf5kodzgz7yvu

Multiple-antenna Placement Delivery Array for Cache-aided MISO Systems [article]

Ting Yang, Kai Wan, Minquan Cheng, Giuseppe Caire
2022 arXiv   pre-print
The objective is to design a coded caching scheme based on uncoded placement and one-shot linear delivery, to achieve the maximum sum Degree-of-Freedom (sum-DoF) with low subpacketization.  ...  and each user is equipped with a local cache of size M files.  ...  [7] , the special (6, 3)-free hypergraphs [8] , the (r, t) Ruzsa-Szeméredi graphs [9] , the strong edge coloring of bipartite graphs [10] , the projective space [11] and other combination design  ... 
arXiv:2201.11462v2 fatcat:sohwnwn34ndvdelawd3q2h6wqm

Some new Constructions of Coded Caching Schemes with Reduced Subpacketization [article]

Wentu Song, Kui Cai, Long Shi
2019 arXiv   pre-print
Our constructions achieve low subpacketization level (e.g., linear subpacketization) with reasonable rate loss and include several known results as special cases.  ...  We study the problem of constructing centralized coded caching schemes with low subpacketization level based on the placement delivery array (PDA) design framework.  ...  In [14] , a class of coded caching schemes with linear file size (i.e., F = K) were constructed from Ruzsa-Szeméredi graphs.  ... 
arXiv:1908.06570v2 fatcat:7xbncaxvdbfohajfcu23upv7ze

Placement Delivery Arrays from Combinations of Strong Edge Colorings [article]

Jerod Michel, Qi Wang
2019 arXiv   pre-print
that subpacketization levels thusly can often be improved.  ...  Theory, 63(9):5821-5833 (2017)], are equivalent to strong edge colorings of bipartite graphs.  ...  In [13] and [14] Shanmugam et al. constructed coded caching schemes with reduced subpacketization levels using Ruzsa-Szemeredi graphs, in [16] Tang and Ramamoorthy discuss an approach using linear  ... 
arXiv:1907.03177v3 fatcat:tbk2yw2izbbgzkqo5umwcubuwa
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