An Upper Bound on the Capacity-Memory Tradeoff of Interleavable Discrete Memoryless Broadcast Channels with Uncoded Prefetching

Abstract

The K-receiver discrete memoryless (DM) broadcast channel (BC) is considered in which each receiver is equipped with a cache memory of the same size. We obtain an upper bound on the capacity-memory tradeoff with uncoded pre-fetching, the highest rate of reliable communication for given cache size. This bound holds for the interleavable DM BC, a class of channels that subsumes the K-receiver degraded DM BC and the three-receiver less noisy DM BC. We then specialize our bound to the Gaussian BC, and show that it is tighter than that recently proposed in the literature for coded pre-fetching for a wide range of cache sizes as would be expected, but the two bounds coincide for sufficiently large cache size. In the two-receiver case, our bound is tight in that it is the exact capacity-memory trade-off with uncoded prefetching which implies that, in this case, coded prefetching does not enhance the capacity-memory tradeoff for sufficiently large cache size.