Improved Converses and Gap Results for Coded Caching

Improved lower bounds are derived on the average and worst case rate-memory tradeoffs of the Maddah-Ali and Niesen-coded caching scenario. For any number of users and files and for arbitrary cache sizes, the multiplicative gap between the exact rate-memory tradeoff and the new lower bound is shown to be less than 2.315 in the worst case scenario and 2.507 in the average-case scenario.