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We study a cache-aided content delivery network consisting of a central server which hosts a catalog of $N$ files, and $K$ caches each with limited memory $M$ which store content related to the files. There are $K$ users, each of which requests a file from the catalog, and has access to the data stored in $L\geq 1$ neighboring caches (with a cyclic wrap-around). The server transmits a common message to all the users, so that each of them can recover their requested file. This setup was recently studied in [1], where a coloring-based placement and coded-delivery policy was proposed and the required server transmission size was shown to be order-optimal with respect to information-theoretic bounds. We propose an alternate index coding-based placement and delivery scheme for this setup, which performs better than the previously proposed strategy. Furthermore, for multiple special cases including the ( $N, K\leq 4, L$ ) and $(N, K, L=K-1)$ -setups, we show that the scheme is exactly optimal under the restriction of uncoded placement. This extends other recent work [2], [3] which studies exact optimality for the single cache-access case ( $L=1$ ) to the multi cache-access case ( $L > 1$ ). |
