Coded Caching for Hierarchical Two-Layer Multi-Access Networks with Low Coding Delay
Rajlaxmi Pandey, Balaji Sundar Rajan · 2024
We consider the two-layer hierarchical coded caching networks, where users connected to each mirror are connected to multiple caches instead of having a dedicated cache. The problem setting involves a server with$N$files connected to$K_{1}$mirrors, each with a cache size of$M_{1}$files, through an error-free bottleneck link, which are further connected to users each one of them can access$r$out of$C$caches each of size$M_{2}$files, available in the system. Each mirror is connected to$\binom{C}{r}$, users, and no two of these users connect to the same set of$r$caches. The total cache size in the system is$\overline{M}=K_{1}M_{1}+K_{1}CM_{2}$called the global memory. The case$r=1$corresponds to hierarchical two-layer systems with users having dedicated caches. Let$R_{1}$be the rate (in the unit of files) of the transmission from the server to the mirrors and$R_{2}$be the rate of transmission from any mirror to the users connected to it that satisfy the demands of all the users. The total delivery time from the server to a user is indicated by the metric$R_{1}+R_{2}$, which is also known as the coding delay. In this work, we present an achievable scheme with low coding delay for a given global memory size. We compare$R_{1}+R_{2}$vs. global memory$\overline{M}=K_{1}M_{1}+K_{1}CM_{2}$of our scheme with other existing schemes for hierarchical two-layer coded caching networks. As we increase$r$, our scheme has a reduction in$R_{1}+R_{2}$, which provides a dual advantage of serving a larger number of users while having a lower coding delay.