Closing the Gap for Coded Caching with Distinct File Sizes
Jinbei Zhang, Xiaojun Lin, Chih-Chun Wang · 2019
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 type1will 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.