From Uncoded Prefetching to Coded Prefetching in Coded Caching Systems

Abstract

In order to characterize the fundamental limit of the tradeoff between the amount of cache memory and the delivery transmission rate in multiuser caching systems, various coding schemes have been proposed. These schemes can largely be categorized into two classes, namely uncoded prefetching schemes and coded prefetching schemes. The significant differences in the coding components between the two classes may leave the impression that they are largely unrelated. In this work, we provide a connection between the uncoded prefetching scheme proposed by Maddah Ali and Niesen (and its improved version by Yu et al.) and the coded prefetching scheme proposed by Tian and Chen. A critical observation is first given where a coding component in the Tian-Chen scheme can be replaced by a binary code, which enables us to view the two schemes as the extremes of a more general scheme. An explicit example is given to show that the intermediate operating points of this general scheme can in fact provide new memory-rate tradeoff points previously not known to be achievable in the literature. This new general coding scheme is then presented and analyzed rigorously, which yields a new inner bound to the memory-rate tradeoff for the caching problem. This inner bound does not have a closed form, but can be computed efficiently using a linear program.