Parallel versus sequential updating for belief propagation decoding

A sequential updating scheme (SUS) for the belief propagation algorithm is proposed, and is compared with the parallel (regular) updating scheme (PUS). Simulation results on various codes indicate that the number of iterations of the belief algorithm for the SUS is about one half of the required iterations for the PUS, where both decoding algorithms have the same error correction properties. The complexity per iteration for both schemes is similar, resulting in a lower total complexity for the SUS, furthermore, the SUS utilizes significantly less memory during the decoding process. We demonstrate that the acceleration in convergence time is related to the inter-iteration information sharing, which is a property of only the SUS, and which increases the "correction gain" per iteration. Finally, the connection between the dynamics of error correcting codes and physical systems is discussed.