The Exact Rate Memory Tradeoff for Small Caches with Coded Placement
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The idea of coded caching was introduced by Maddah-Ali and Niesen who demonstrated the advantages of coding in caching problems. To capture the essence of the problem, they introduced the (N, K) canonical cache network in which K users with independent caches of size M request files from a server that has N files. Among other results, the caching scheme and lower bounds proposed by them led to a characterization of the exact rate memory tradeoff when M≥N/K(K-1). These lower bounds along with the caching scheme proposed by Chen et al. led to a characterization of the exact rate memory tradeoff when M≤1/K. In this paper we focus on small caches where M∈[0,N/K] and derive new lower bounds. For the case when ⌈K+1/2⌉≤ N ≤ K and M∈[1/K,N/K(N-1)], our lower bounds demonstrate that the caching scheme introduced by Gómez-Vilardebó is optimal and thus extend the characterization of the exact rate memory tradeoff. For the case 1≤ N≤⌈K+1/2⌉, we show that the new lower bounds improve upon the previously known lower bounds.
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