Subexponential and Linear Subpacketization Coded Caching via Line Graphs and Projective Geometry
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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 be divisible into a large number of parts (this number is called subpacketization). In fact, most schemes require the subpacketization to be growing asymptotically as exponential in some r^th root of the number of users K. On the other extreme, few schemes having subpacketization linear in K are known; however they require large number of users to exist, or they offer only little gain in rate. 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 low subpacketization and moderate rate gains. Both the schemes achieve the same asymptotic subpacketization, which is exponential in O((log K)^2) (thus improving on the root-of-K exponent). The first scheme has a larger cache requirement but has at most a constant rate (with increasing K), while the second has small cache requirement but has a larger rate. As a special case of our second scheme, we get a new linear subpacketization scheme, which has a more flexible range of parameters than existing linear subpacketization schemes. We also present two new lower bounds on the optimal rate of coded caching for a given subpacketization level. Extending our techniques, we also obtain low subpacketization schemes for other multi-receiver settings such as D2D communications, distributed computing, and the cache-aided interference channel. We validate the performance of all our schemes via extensive numerical comparisons.
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