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IEEE Communications Letters

Trapping Set Error Correction through Adaptive Informed Dynamic Scheduling Decoding of LDPC Codes

Saejoon Kim

Published Jul 1, 2012• 8 citations
Publisher

Abstract

Recent studies indicate that sequential scheduling of iterative decoding of low-density parity-check codes can provide improved code performance in comparison with the conventional flooding in terms of decoding success rate and convergence speed. In particular, a class of sequential scheduling schemes known as informed dynamic scheduling (IDS) has shown to outperform other sequential scheduling schemes from its capability to correct trapping set errors. In this letter, we present an adaptive IDS scheme which combines and outperforms previously proposed sequential scheduling schemes.

DOI
10.1109/lcomm.2012.050112.120262

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Recent studies indicate that sequential scheduling of iterative decoding of low-density parity-check codes can provide improved code performance in comparison with the conventional flooding in terms of decoding success rate and convergence speed. In particular, a class of sequential scheduling schemes known as informed dynamic scheduling (IDS) has shown to outperform other sequential scheduling schemes from its capability to correct trapping set errors. In this letter, we present an adaptive IDS scheme which combines and outperforms previously proposed sequential scheduling schemes.
Low-Density Parity-Check (LDPC) codes are usually decoded by running an iterative belief-propagation (BP), or message-passing, algorithm over the factor graph of the code. The traditional message-passing scheduling, called flooding, 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 introduces the problem of finding the best sequence of message updates. We propose Informed Dynamic Scheduling (IDS) strategies that select the message-passing schedule according to the observed rate of change of the messages. In general, IDS strategies require computation to select the message to update but converge in fewer message updates because they focus on the part of the graph that has not converged. Moreover, IDS yields a lower error-rate performance than either flooding or sequential scheduling because IDS strategies overcome traditional trapping-set errors. This paper presents IDS strategies that address several issues including performance for short-blocklength codes, complexity, and implementability.
Low-Density Parity-Check (LDPC) codes are usually decoded by running an iterative belief-propagation (BP), or message-passing, algorithm over the factor graph of the code. The message-passing schedule of the BP algorithm significantly affects the performance of the LDPC decoder. The authors recently presented a novel message-passing schedule, called Informed Dynamic Scheduling (IDS), that selects the message-passing schedule according to the observed rate of change of the messages. IDS yields a lower error-rate performance than traditional message-passing schedules (such as flooding and LBP) because it solves traditional trapping-set errors. However, for short-blocklength LDPC codes, IDS algorithms present non-trapping-set errors in the error floor region. This paper presents a careful analysis of those errors and proposes mixed scheduling strategies, combining LBP with IDS, that solve these non-trapping-set errors. Also, we will show that some lower-complexity techniques, such as mixed scheduling, perform close to the best IDS strategies for larger-blocklength codes.
Low-density parity-check (LDPC) codes offer excellent performance at competitive levels of complexity. Short block length LDPC codes avoid the large processing latency incurred by the large block lengths classically considered for this class of codes, making them a potential candidate for next generation wireless communications systems. In this paper, a novel informed dynamic scheduling (IDS) approach for decoding LDPC codes is developed based on the use of the current message reliabilities and the residuals of the potential updates to select the messages passed in the graph during iterative Sum Product decoding. An alternative measure of the iteration of the IDS schemes is also proposed which highlights the high cost of those algorithms in terms of processing complexity and motivates the development of the proposed approach. The proposed Rel.-RBP decoding algorithm offers very fast convergence at reduced complexity and gains in error rate performance when compared to the previous schemes.
Recent studies have shown that sequential belief propagation decoding of low-density parity-check codes can increase the decoding convergence speed while simultaneously improving the asymptotic performance compared to the conventional flooding scheme. Two of the practical sequential decoding schemes known are the ones by Casado et al. [1] in which informed dynamic scheduling is used for scheduling the sequential updates of the messages. In this letter, we propose a two-staged informed dynamic scheduling that unifies and outperforms the two schemes of [1].
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.