  In this paper, we consider a multi-access coded caching system with
decentralized prefetching, where a server hosts $N$ files, each of size $F$
bits, and is connected to $K$ users through a shared link. There are $c$ caches
distributed across the network and each of the $K$ users connects to a random
set of $r\leq c$ caches. Initially, we consider the model in which each of the
cache subsets is accessed by exactly a specific number of users. For this
model, a novel linear delivery scheme is introduced, using which the
closed-form expression for the per-user delivery rate is computed. Furthermore,
using techniques from index coding, the optimality of the proposed linear
delivery scheme among all linear delivery schemes is proved. The results of the
decentralized shared caching and conventional decentralized caching schemes are
recovered as special cases of the proposed model. The model is further
generalized by allowing each cache subset to serve any number of users. This
enhances the flexibility of the system, enabling it to accommodate any
arbitrary number of users. A delivery scheme is proposed for the generalized
model and is shown to be optimal for certain user-to-cache associations.
