Coded Caching based on Combinatorial Designs

Abstract

We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called cache) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, introduced in [1], 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. Starting from [1], 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 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( 1 √ K ) or Θ( 1 K ), K being the number of users), they provide a rate that is either constant or decreasing (O( 1 K )) with increasing K, and moreover require competitively small levels of subpacketization (being O(K i ), 1 ≤ i ≤ 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.

Maddah-Ali-Niesen Scheme for Multi-access Coded Caching

“…1 with b = K and z = 1 which may be viewed as each user having a dedicated cache of its own. To mitigate the exponential subpacketization problem that arises, by employing the MaN scheme several other schemes based on resolvable block designs from linear block codes [10], hypergraphs [11], block designs [12], schemes in [13] etc., have also been proposed in the recent years. These approaches have helped to reduce the subpacketization problem, by mainly trading off with respect to rate or memory fraction accessible to the user as compared to the scheme in [1].…”

Improving Placement Delivery Array Coded Caching Schemes With Coded Placement

“…There are also many other results on PDA such as [8], [9], [17]. Very recently there are several schemes with low subpacketization such as [10], [11], which can be represented by PDAs.…”

Improved Multi-access Coded Caching Schemes From Cross Resolvable Designs

“…The main focus of coded caching is in designing schemes with reduced rate and practical subpacketization levels. Over the years there have been many approaches aimed at reducing subpacketization levels that involved developing coded caching schemes from resolvable designs from linear block codes [2], block designs [3], placement delivery arrays [4]. While the focus has been mostly on setups with users equipped with dedicated caches, the setups where users have to share caches is also of utmost interest [5] [6] [7].…”