The Optimal Rate Memory Tradeoff in Multi-Access Coded Caching: Large Cache Size
Vijith Kumar K P, Brijesh Kumar Rai, Tony Jacob · 2023
In this paper, we consider the (N,K,L) multi-access caching network where K users and K caches are connected to a server with N files, each of size F bits, through a shared error-free broadcast channel. Each user has access to L nearby caches, each of size MF bits, in a cyclic wrap-around manner. Even after several previous attempts, the exact characterization of the optimal rate memory tradeoff is still an open problem except in the case where L = K − 1 and L = 1 with large cache $M \in \left[ {\frac{N}{L} \cdot \frac{{K - 1}}{K},\frac{N}{L}} \right]$. This paper determines the optimal rate memory tradeoff for the cache network with L = K − 2 and $M \in \left[ {\frac{N}{{K - 2}} \cdot \frac{{K - 1}}{K},\frac{N}{{K - 2}}} \right]$. This is done by proposing a new caching scheme that operates at the memory rate pair $\left( {\frac{N}{{K - 2}},\frac{{K - 1}}{K},\frac{1}{K}} \right)$ and deriving a set of lower bounds to demonstrate the optimality of the scheme.