Abstract A scheme for deterministic simulation of the PRAM on the Module Parallel Computer or on Bounded Degree Networks is described. The scheme requires only a constant memory blowup, thus achieving better memory utilization than previously known. The new method is also free from the need of time stamps, which were a basic element of all previous schemes. These improvements are achieved by adopting error-correcting codes techniques. We consider several coding methods and derive trade-offs between memory utilization, run time, and the size of the PRAM shared memory.