Improved Lower Bounds for Multi-Access Coded Caching
K. K. Krishnan Namboodiri, Balaji Sundar Rajan · IEEE Transactions on Communications · 2022
The multi-access variant of the coded caching problem with$N$files,$K$users and$K$caches, where each user has access to$L$neighbouring caches in a cyclic wrap-around manner, is considered. A cut-set based lower bound on the optimal rate-memory trade-off of the multi-access coded caching (MACC) scheme is derived. Furthermore, an improved lower bound on the optimal rate-memory trade-off of the MACC scheme is derived using non-cut-set arguments. The improved lower bound is tighter than the previously known lower bounds for the same setting. Further, for cache memory$M\leq {(N-K+L)}/{K}$, an achievable scheme makes use of coded placement is presented. By matching with the improved lower bound, the scheme is shown to be optimal when$N\leq K$. Also, lower bounds on the optimal rate-memory trade-off of the MACC scheme incorporating secure delivery and secrecy conditions are derived.