Closing the Gap for Coded Caching with Distinct File Sizes

Coded caching can exploit multicast opportunities even when multiple users request different pieces of content, and thus can significantly reduce the backhaul requirement to serve high-volume content. A common assumption in existing studies of coded caching is that all files are with the same size, which however may not be true in reality. Our previous work [1] first studied this problem, and proposed a non-trivial lower bound, as well as a new achievable scheme that uses a caching probability increasing proportionally with the file size. However, the gap [1] of the achievable rate and the lower bound still differs by a factor of Θ(log K), where K is the number of users in the system. In this paper, under a mild assumption that the total size of all files is larger than eight times the size of one individual cache, we will close this gap and reduce it to a constant by proposing a novel new lower bound and another new achievable scheme. Our lower bound is derived by considering a new cut-set bound, where files of a type
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will be requested more often if the number of such files is smaller. Our achievable scheme uses a caching probability that decreases with the number of files with a same type. The improvements on both the lower bound and the achievable rate make their gap constant.