Rate-Memory Trade-off for Multi-access Coded Caching with Uncoded Placement
This work improves theoretical bounds for caching systems in communication networks, though it is incremental as it builds on prior index coding mappings and restricts to uncoded placement.
The paper tackles the rate-memory trade-off in a multi-access coded caching system with uncoded placement, deriving new achievable rates and lower bounds that reduce the multiplicative gap to at most 2 for cases where each user accesses at least half the caches, establishing order-optimality.
We study a multi-access variant of the popular coded caching framework, which consists of a central server with a catalog of $N$ files, $K$ caches with limited memory $M$, and $K$ users such that each user has access to $L$ consecutive caches with a cyclic wrap-around and requests one file from the central server's catalog. The server assists in file delivery by transmitting a message of size $R$ over a shared error-free link and the goal is to characterize the optimal rate-memory trade-off. This setup was studied previously by Hachem et al., where an achievable rate and an information-theoretic lower bound were derived. However, the multiplicative gap between them was shown to scale linearly with the access degree $L$ and thus order-optimality could not be established. A series of recent works have used a natural mapping of the coded caching problem to the well-known index coding problem to derive tighter characterizations of the optimal rate-memory trade-off under the additional assumption that the caches store uncoded content. We follow a similar strategy for the multi-access framework and provide new bounds for the optimal rate-memory trade-off $R^*(M)$ over all uncoded placement policies. In particular, we derive a new achievable rate for any $L \ge 1$ and a new lower bound, which works for any uncoded placement policy and $L \ge K/2$. We then establish that the (multiplicative) gap between the new achievable rate and the lower bound is at most $2$ independent of all parameters, thus establishing an order-optimal characterization of $R^*(M)$ for any $L\ge K/2$. This is a significant improvement over the previously known gap result, albeit under the restriction of uncoded placement policies. Finally, we also characterize $R^*(M)$ exactly for a few special cases.