Combination Network with Multiaccess Caching

In the traditional $(H,r,M,N)$ combination network, a central server storing N files communicates with $K=(\genfrac{}{}{0pt}{}{H}{r})$ users through H cache-less relays. Each user has a local cache of size M files and is connected to a distinct subset of r relays. This paper studies the $(H,r,L,\mathrm{\Lambda },M,N)$ combination network with multi-access caching, where $\mathrm{\Lambda }$ cache nodes (each of size M files) are available and each user can access L cache nodes. We show that in the regime $H\ge \mathrm{\Lambda }$ and $r\ge L$, an achievable design can be obtained via a group-wise operation, which reduces the scheme design within each group to an effective $(\mathrm{\Lambda },L,L,\mathrm{\Lambda },M,N)$ instance. For the case $\mathrm{\Lambda }=H$ and $L=r$, we further propose an explicit coded caching scheme constructed via two array-based representations (a cache-node placement array and a user-retrieve array) and a derived combinatorial placement delivery array (CPDA) based on the Maddah-Ali–Niesen (MN) placement strategy. Numerical comparisons using the user-retrievable cache ratio as the evaluation metric indicate that the proposed scheme approaches the converse bound of the traditional combination network, and the performance gap diminishes as the cache ratio increases.