288 research outputs found

    Coded Caching via Line Graphs of Bipartite Graphs

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    We present a coded caching framework using line graphs of bipartite graphs. A clique cover of the line graph describes the uncached subfiles at users. A clique cover of the complement of the square of the line graph gives a transmission scheme that satisfies user demands. We then define a specific class of such caching line graphs, for which the subpacketization, rate, and uncached fraction of the coded caching problem can be captured via its graph theoretic parameters. We present a construction of such caching line graphs using projective geometry. The presented scheme has a rate bounded from above by a constant with subpacketization level qO((logqK)2)q^{O((log_qK)^2)} and uncached fraction Θ(1K)\Theta(\frac{1}{\sqrt{K}}), where KK is the number of users and qq is a prime power. We also present a subpacketization-dependent lower bound on the rate of coded caching schemes for a given broadcast setup.Comment: Keywords: coded caching based on projective geometry over finite field

    Coded Caching based on Combinatorial Designs

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    We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called \textit{cache}) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. In this work, we propose a binary matrix model to construct the coded caching scheme. The ones in such a \textit{caching matrix} indicate uncached subfiles at the users. Identity submatrices of the caching matrix represent transmissions in the delivery phase. Using this model, we then propose several novel constructions for coded caching based on the various types of combinatorial designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement (uncached fraction being Θ(1K)\Theta(\frac{1}{\sqrt{K}}) or Θ(1K)\Theta(\frac{1}{K}), KK being the number of users), they provide a rate that is either constant or decreasing (O(1K)O(\frac{1}{K})) with increasing KK, and moreover require competitively small levels of subpacketization (being O(Ki),1≀i≀3O(K^i), 1\leq i\leq 3), which is an extremely important parameter in practical applications of coded caching. We mark this work as another attempt to exploit the well-developed theory of combinatorial designs for the problem of constructing caching schemes, utilizing the binary caching model we develop.Comment: 10 pages, Appeared in Proceedings of IEEE ISIT 201

    Simplifying Wireless Social Caching

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    Social groups give the opportunity for a new form of caching. In this paper, we investigate how a social group of users can jointly optimize bandwidth usage, by each caching parts of the data demand, and then opportunistically share these parts among themselves upon meeting. We formulate this problem as a Linear Program (LP) with exponential complexity. Based on the optimal solution, we propose a simple heuristic inspired by the bipartite set-cover problem that operates in polynomial time. Furthermore, we prove a worst case gap between the heuristic and the LP solutions. Finally, we assess the performance of our algorithm using real-world mobility traces from the MIT Reality Mining project dataset and two mobility traces that were synthesized using the SWIM model. Our heuristic performs closely to the optimal in most cases, showing a better performance with respect to alternative solutions.Comment: Parts of this work were accepted for publication in ISIT 2016. A complete version is submitted to Transactions on Mobile Computin
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