An efficient multiple-groupcast coded multicasting scheme for finite fractional caching

Coded multicasting has been shown to improve the caching performance of content delivery networks with multiple caches downstream of a common multicast link. However, the schemes that have been shown to achieve order-optimal performance require content items to be partitioned into a number of packets that grows exponentially with the number of users [1]. In this paper, we first extend the analysis of the order-optimal multiple-groupcast coded multicasting scheme in [2] to the case of heterogeneous cache sizes and demand distributions, providing an achievable scheme and an upper bound on the optimal performance when the number of packets goes to infinity. We then show that the scheme achieving this upper bound can very quickly loose its promising multiplicative caching gain for finite content packetization. To overcome this limitation, we design a novel polynomial-time algorithm based on greedy local graph-coloring that, while keeping the same content packetization, recovers a significant part of the multiplicative caching gain. Our results show that the achievable schemes proposed to date to quantify the fundamental limiting performance, must be properly designed for practical regimes of finite content packetization.