Combinatorial Multi-Access Coded Caching with Private Caches

We consider a variant of the coded caching problem where users connect to two types of caches, called private and access caches. The problem setting consists of a server with a library of files and a set of access caches. Each user, equipped with a private cache, connects to a distinct <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r$</tex>-subset of the access caches. For this setting, we provide a coded caching scheme and derive a lower bound on the number of transmissions for this scheme. We also present lower and upper bounds for the optimal worst-case rate under uncoded placement for this setting using the rates of the Maddah-Ali-Niesen scheme for dedicated and combinatorial multi-access coded caching settings, respectively. Further, we derive a lower bound on the optimal worst-case rate for any general placement policy using cut-set arguments. Numerical plots comparing the rate of the proposed achievability scheme with the above bounds are also provided, from which it can be observed that the proposed scheme approaches the lower bound in the large-memory regime.