On the Optimality of Two Decentralized Coded Caching Schemes With and Without Error Correction
Nujoom Sageer Karat, Kodi Lakshmi Vijith Bhargav, Balaji Sundar Rajan · 2020
The decentralized coded caching was Introduced In [M. A. Maddah-Ali and U. Niesen, "Decentralized coded caching attains order-optimal memory-rate tradeoff," IEEE/ACM Trans. Networking, Aug. 2015] in which no coordination is required for the content placement. This scheme is extended to all the demand cases and the optimality is shown in the literature under the uncoded prefetching regime using information theoretic lower bound. In this paper, an alternate proof for optimality is given using index coding techniques. Moreover, for the case when the shared broadcast link is error prone, an optimal error correcting delivery scheme is proposed for coded caching problems with the decentralized placement. Next, the Least Recently Sent (LRS) online coded caching scheme is considered. The optimality of this scheme is also proved using index coding techniques. An optimal error correcting delivery scheme is proposed for coded caching problems with the LRS online prefetching.