Coded Caching with Heterogeneous Cache Sizes and Link Qualities: The Two-User Case

Abstract

The centralized coded caching problem is studied under heterogeneous cache sizes and channel qualities from the server to the users, focusing on the two-user case. A server holding N files is considered to be serving two users with arbitrary cache capacities of M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and it is assumed that in addition to a shared common link, each user also has a private link from the server available during the delivery phase. Optimal caching and delivery strategies that minimize the worst-case delivery latency are presented for an arbitrary N. The converse proof benefits from Tian's observation that it suffices to consider file-index symmetric caching schemes, while the achievability is obtained through memory-sharing among certain special (M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) pairs. The optimal scheme is shown to exploit the private link capacities by transmitting part of the corresponding user's request in an uncoded fashion. When there are no private links, the results presented here improve upon the two known results in the literature, namely, i) equal cache capacities and arbitrary number of files; and ii) unequal cache capacities and N = 2 files.