A novel informed fixed scheduling (IFS) scheme for shuffled belief-propagation (BP) decoding of binary low-density parity-check (LDPC) code is introduced to improve the BP decoding convergence. The IFS finds an appropriate order of variable nodes in accordance with the number of updated neighbors in the code graph, ensuring that the maximum number of latest message updates is utilized within a single iteration. This allows the utilization of most reliable message updates in a timely manner, leading to faster error-rate convergence. Simulation results show that the proposed IFS scheme improves the convergence speed of BP decoder by up to 20% for regular LDPC codes and 45% for irregular LDPC codes, without affecting the error-rate performance, at medium-to-high signal-to-noise ratio over binary-input additive white Gaussian noise channel.
A novel informed fixed scheduling (IFS) scheme for shuffled belief-propagation (BP) decoding of binary low-density parity-check (LDPC) code is introduced to improve the BP decoding convergence. The IFS finds an appropriate order of variable nodes in accordance with the number of updated neighbors in the code graph, ensuring that the maximum number of latest message updates is utilized within a single iteration. This allows the utilization of most reliable message updates in a timely manner, leading to faster error-rate convergence. Simulation results show that the proposed IFS scheme improves the convergence speed of BP decoder by up to 20% for regular LDPC codes and 45% for irregular LDPC codes, without affecting the error-rate performance, at medium-to-high signal-to-noise ratio over binary-input additive white Gaussian noise channel.
In this letter, a novel scheduling scheme for decoding irregular low-density parity-check (LDPC) code, based on the column weight of variable nodes in the code graph, is introduced. In this scheme, the irregular LDPC code is decoded using the shuffled belief-propagation (BP) algorithm by selecting the variable nodes in descending order of their column weight. Via numerical simulation, it is shown that the proposed high-to-low column-weight based decoding schedule can noticeably increase the convergence speed at medium to high signal-to-noise ratio (SNR) over AWGN and Rayleigh fading channels without introducing additional complexity or error rate degradation. Furthermore, it is found that the improvement in decoding convergence is proportional to the maximum column-weight in the code graph.
Low-density parity-check (LDPC) codes have proved to be very powerful channel coding schemes with a broad range of applications. However, as maximum-likelihood decoding is utterly complex, suboptimal decoders have to be employed. One of the most popular decoding algorithms of LDPC codes is belief propagation (BP) decoding. In this paper, we present a novel scheduling for belief propagation decoding of LDPC codes. The new approach combines probabilistic scheduling with the known shuffled and check-shuffled serial scheduling algorithms. The resulting probabilistic shuffled and probabilistic check-shuffled decoders show a superior performance in terms of residual bit error rate. The drawback is that the convergence speed is slightly decreased. However, the convergence is still faster than for the standard and probabilistic flooding algorithms. Furthermore, we have adapted the probabilistic flooding schedule and the proposed probabilistic shuffled schedule to the non-binary case. We show that the aforementioned effects on the binary decoder can similarly be observed when applying the different schedules to the decoding of LDPC codes over higher order Galois fields.
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.
Schedule plays an important role in layered belief propagation (BP) decoding of low-density parity-check (LDPC) codes. It affects the error-rate performance as well as convergence rate of the decoder. In this paper, an efficient scheduling scheme is proposed to arrange the updating order of check nodes for layered BP decoder of regular LDPC codes. This scheme selects check node one at a time based on the reliability of the variable nodes. Specifically each time the check node with maximum number of low-reliability neighbors is selected. For simplicity, we introduce the updating state instead of the real-time messages to represent variable-node reliability. Simulation results on regular LDPC codes prove that the proposed scheduling scheme can obtain efficient schedules with fast convergence and good error-rate performance.
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.
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.