By adding some functions to memories, highly parallel computation may be realized. We have proposed memory-based parallel computation models, which uses a new functional memory as a SIMD type parallel computation engine. In this paper, we consider models with communication between the words of the functional memory. The memory-based parallel computation model consists of a random access machine and a functional memory. On the functional memory, it is possible to access multiple words in parallel according to the partial match with their memory addresses. The cube-FRAM model, which we propose in this paper, has a hypercube network on the functional memory. We prove that PSPACE is accelerated to polynomial time on the model. We think that the operations on each word of the functional memory are, in a sense, the essential ones for SIMD type parallel computation to realize the computational power.