Coded Caching Schemes for Multiaccess Topologies via Combinatorial Design

This paper studies a multiaccess coded caching (MACC) problem where the connectivity topology between the users and the caches can be described by a class of combinatorial designs. Our model includes several MACC topologies considered in previous works as special cases. The considered MACC network includes a server containing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> files, Γ cache nodes and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> cacheless users, where each user can access <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> cache nodes. The server is connected to the users via an error-free shared link, while the users can directly access the content in their connected cache nodes. Our goal is to minimize the worst-case transmission load on the shared link in the delivery phase. The main limitation of the existing MACC works is that only some specific access topologies are considered, including the only cases where the number of users <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> scales either linearly or exponentially in Γ. We overcome this limitation by formulating a new access topology derived from two classical combinatorial structures, referred to as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i>-design and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i>-group divisible design. By leveraging the properties of these combinatorial structures, we propose two classes of coded caching schemes for a flexible number of users, where the number of users can scale linearly, polynomially or exponentially with the number of cache nodes. As a by-product, by extending the proposed scheme to the original dedicated coded caching scenario (i.e., each user has its own cache), the resulting scheme can unify several existing coded caching schemes.