  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
perfor- mance 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 achievable scheme in [2] to the case of
heterogeneous cache sizes and demand distribu- tions, providing an achievable
scheme and an upper bound on the limiting average performance when the number
of packets goes to infinity while the remaining system parameters are kept
constant. We then show how the scheme achieving this upper bound can very
quickly loose its 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
limiting performance, must be properly designed for practical finite system
parameters.
