Coded caching for files with distinct file sizes

Coded caching can exploit new multicast opportunities even when multiple users request different pieces of content, and thus can significantly reduce the backhaul requirement for serving high-volume content. However, existing studies of coded caching have been limited to the scenarios where all files of interest are of a common size. This work studies the performance limits of coded caching when the file sizes are different. We derive a new lower bound and an achievable upper bound for the worst-case transmission rate under coded caching, and show that these two bounds differ by at most a Θ(log K) factor, where K is the number of users in the system. There are two key novelties in our analysis. First, our lower bound is derived by considering a new cut-set bound where larger files are requested more times. The analysis of this new cut-set bound requires careful concatenation of several entropy inequalities. Compared to a lower bound using standard cut-set arguments, our lower bound is improved by a Θ(log K) factor. Second, our achievable scheme uses a caching probability that increases proportionally with the file size. Compared to schemes that use a common caching probability, the achievable rate of our scheme is reduced by a Θ K/log_k² factor.