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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