A complexity reducing method for iterative message passing decoding algorithms of low-density parity-check (LDPC) codes is described. It is based on lazy scheduling which involves a partial update of messages in the iterations. A density evolution (DE) approach is developed for optimization of the parameters for choice of the messages to be updated. Combined with an efficient serial scheduling, the resulting method reduces the decoding complexity by about 70-75% compared to the classical belief propagation (BP) scheme, while maintaining the same performance
A complexity reducing method for iterative message passing decoding algorithms of low-density parity-check (LDPC) codes is described. It is based on lazy scheduling which involves a partial update of messages in the iterations. A density evolution (DE) approach is developed for optimization of the parameters for choice of the messages to be updated. Combined with an efficient serial scheduling, the resulting method reduces the decoding complexity by about 70-75% compared to the classical belief propagation (BP) scheme, while maintaining the same performance
An efficient decoding schedule for low-density parity-check (LDPC) codes that outperforms the conventional approach, in terms of both complexity and performance, is presented. Conventionally, in each iteration, all symbol nodes and, subsequently, all the check nodes, send messages to their neighbors ("flooding schedule"). In contrast, in the proposed method, the updating of nodes is performed according to a serial schedule which propagates the information twice as fast. A density evolution (DE) algorithm for asymptotic analysis of the new schedule is derived, showing that, when working near the code's capacity, the decoder converges in approximately half the number of iterations. In addition, a concentration theorem is proved, showing that, for a randomly chosen serial schedule, code graph, and decoder input, the decoder's performance approaches its expected one as predicted by the DE algorithm, when the code length increases.
Abstract — Low-Density Parity-Check (LDPC) codes are usually decoded by running an iterative belief-propagation, or message-passing, algorithm over the factor graph of the code. The traditional message-passing schedule consists of updating all the variable nodes in the graph, using the same pre-update information, followed by updating all the check nodes of the graph, again, using the same pre-update information. Recently several studies show that sequential scheduling, in which messages are generated using the latest available information, significantly improves the convergence speed in terms of number of iterations. Sequential scheduling raises the problem of finding the best sequence of message updates. This paper presents practical scheduling strategies that use the value of the messages in the graph to find the next message to be updated. Simulation results show that these informed update sequences require significantly fewer iterations than standard sequential schedules. Complexity and implementability issues are also addressed. Index Terms — Belief propagation-algorithm, messagepassing schedule, error-control codes, low-density paritycheck codes. I.
Conventionally, in each low-density parity-check (LDPC) decoding iteration all the variable nodes and subsequently all the check nodes send messages to their neighbors (flooding schedule). An alternative, more efficient, approach is to update the nodes' messages serially (serial schedule). A theoretical analysis of serial message passing decoding schedules is presented. In particular, the evolution of the computation tree under serial scheduling is analyzed. It shows that the tree grows twice as fast in comparison to the flooding schedule's one, indicating that the serial schedule propagates information twice as fast in the code's underlying graph. Furthermore, an asymptotic analysis of the serial schedule's convergence rate is done using the density evolution (DE) algorithm. Applied to various ensembles of LDPC codes, it shows that for long codes the serial schedule is expected to converge in half the number of iterations compared to the standard flooding schedule, when working near the ensemble's threshold. This observation is generally proved for the binary erasure channel (BEC) under some natural assumptions. Finally, an accompanying concentration theorem is proved.
An efficient dynamic schedule for layered belief-propagation (LBP) decoding of low-density parity-check (LDPC) codes is presented, in which the check nodes connecting to a variable node with maximum relative message residual are chosen in each dynamic decoding iteration, and then LBP is performed for these check nodes. In this schedule we combined the features of lazy schedule and node-wise residual belief propagation (NWRBP) together while keeping the extra computational complexity very low. Simulation results show that the new schedule speeds up the convergence rate and greatly improves error performance at medium to high signal-to-noise ratio (SNR) when compared to the standard LBP decoding algorithm.
Low-density parity-check (LDPC) codes are usually decoded by running an iterative belief-propagation, or message-passing, algorithm over the factor graph of the code. The traditional message-passing schedule consists of updating all the variable nodes in the graph, using the same pre-update information, followed by updating all the check nodes of the graph, again, using the same pre-update information. Recently several studies show that sequential scheduling, in which messages are generated using the latest available information, significantly improves the convergence speed in terms of number of iterations. Sequential scheduling raises the problem of finding the best sequence of message updates. This paper presents practical scheduling strategies that use the value of the messages in the graph to find the next message to be updated. Simulation results show that these informed update sequences require significantly fewer iterations than standard sequential schedules. Furthermore, the paper shows that informed scheduling solves some standard trapping set errors. Therefore, it also outperforms traditional scheduling for a large numbers of iterations. Complexity and implementability issues are also addressed.
Beside the well known iterative Belief Propagation algorithm several alternative decoding schemes for Low-Density Parity-Check (LDPC) codes providing better performance in terms of residual error rate, convergence speed or computational complexity have been developed in the last years. Recently, Informed Dynamic Scheduling has been proposed in [1] providing different decoding strategies that dynamically decide which messages are passed throughout the decoding process. It was shown that the overall convergence can be sped up considerably and also more errors can be corrected compared to other (non-dynamic) decoding strategies. However, these improvements are somehow overshadowed by a significant amount of additional computational complexity that is needed for the selection of the messages to be updated in each decoding step. We propose two novel dynamic decoding strategies that allow for a flexible adaptation of the decoder's dynamics and reduce the additional complexity remarkably while maintaining, and in some cases even exceeding, the convergence speed and error rate performance of currently known dynamic schedules.