Abstract-Low-Density Parity-Check (LDPC) codes are usually decoded by running an iterative belief-propagation algorithm over the factor graph of the code. In the traditional messagepassing schedule, in each iteration all the variable nodes, and subsequently all the factor nodes, pass new messages to their neighbors. Recently several studies show that serial scheduling, in which messages are generated using the latest available information, significantly improves the convergence speed in terms of number of iterations. It was observed experimentally in several studies that the serial schedule converges in exactly half the number of iterations compared to the standard parallel schedule. In this correspondence we provide a theoretical motivation for this observation by proving it for single-path graphs.
A sequential updating scheme (SUS) for belief propagation (BP) decoding of LDPC codes over Galois fields, GF (q), and correlated Markov sources is proposed, and compared with the standard parallel updating scheme (PUS). A thorough experimental study of various transmission settings indicates that the convergence rate, in iterations, of the BP algorithm (and subsequently its complexity) for the SUS is about one half of that for the PUS, independent of the finite field size q. Moreover, this 1/2 factor appears regardless of the correlations of the source and the channel's noise model, while the error correction performance remains unchanged. These results may imply on the 'universality' of the one half convergence speed-up of SUS decoding.
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