# The Exact Rate Memory Tradeoff for Large Caches with Coded Placement

The idea of coded caching for content distribution networks was introduced by Maddah-Ali and Niesen, who considered the canonical (N, K) cache network in which a server with N files satisfy the demands of K users (equipped with independent caches of size M each). Among other results, their work provided a characterization of the exact rate memory tradeoff for the problem when M≥N/K(K-1). In this paper, we improve this result for large caches with M≥N/K(K-2). For the case ⌈K+1/2⌉≤ N ≤ K, we propose a new coded caching scheme, and derive a matching lower bound to show that the proposed scheme is optimal. This extends the characterization of the exact rate memory tradeoff to the case M≥N/K(K-2+(K-2+1/N)/(K-1)). For the case 1≤ N≤⌈K+1/2⌉, we derive a new lower bound, which demonstrates that the scheme proposed by Yu et al. is optimal and thus extend the characterization of the exact rate memory tradeoff to the case M≥N/K(K-2).

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