On the Optimality of Ali-Niesen Decentralized Coded Caching Scheme With and Without Error Correction

The decentralized coded caching was introduced in [M.~A. Maddah-Ali and U.~Niesen, `Decentralized coded caching attains order-optimal memory-rate tradeoff,' \emph{IEEE/ACM Trans. Networking}, vol.~23, no.~4, pp. 1029--1040, Aug. 2015] in which no coordination is required for the content placement. In this paper, with $N$ files and $K$ users, first it is shown that the decentralized coded caching scheme of Ali and Niesen is optimal for $N \geq K$ using techniques from index coding. Next the case when the shared link is error prone is considered. For this case, an optimal error correcting delivery scheme is proposed for coded caching problems with decentralized placement. Expression for the worst case rate is obtained when there are finite number of transmissions in error.