We propose two new decoding algorithms for low-density parity-check (LDPC) codes. The Consensus and Return residual belief propagation (C&R-RBP) algorithm reduces the number of iterations required to achieve a target decoding error rate over an AWGN channel by exploiting the availability of updated information, thereby mitigating the performance degradation caused by the greedy behavior of RBP-based algorithms and reducing error propagation. The Consensus and Delayed Return RBP algorithm (C&DR-RBP) achieves better performance in the early decoding iterations than C&R-RBP, making it particularly suitable for low-latency applications. Both proposed methods maintain the same computational complexity as the original RBP algorithm in terms of residual calculations. We also provide a formal analysis showing that the Consensus mechanism increases the probability of correct bit decisions under initial decoding conditions and in the presence of severe bit transmission errors, providing insight into the performance gains observed in the simulations. Numerical results based on the rapidly growing 5G New Radio (NR) standard, considering different code lengths, code rates, and channel models, demonstrate that both methods outperform competing RBP-based algorithms with similar overall computational complexity in terms of frame error rate (FER) and bit error rate (BER). In particular, among all the algorithms considered, C&DR-RBP requires the fewest iterations to achieve a given error rate.
We propose two new decoding algorithms for low-density parity-check (LDPC) codes. The Consensus and Return residual belief propagation (C&R-RBP) algorithm reduces the number of iterations required to achieve a target decoding error rate over an AWGN channel by exploiting the availability of updated information, thereby mitigating the performance degradation caused by the greedy behavior of RBP-based algorithms and reducing error propagation. The Consensus and Delayed Return RBP algorithm (C&DR-RBP) achieves better performance in the early decoding iterations than C&R-RBP, making it particularly suitable for low-latency applications. Both proposed methods maintain the same computational complexity as the original RBP algorithm in terms of residual calculations. We also provide a formal analysis showing that the Consensus mechanism increases the probability of correct bit decisions under initial decoding conditions and in the presence of severe bit transmission errors, providing insight into the performance gains observed in the simulations. Numerical results based on the rapidly growing 5G New Radio (NR) standard, considering different code lengths, code rates, and channel models, demonstrate that both methods outperform competing RBP-based algorithms with similar overall computational complexity in terms of frame error rate (FER) and bit error rate (BER). In particular, among all the algorithms considered, C&DR-RBP requires the fewest iterations to achieve a given error rate.
We propose two new decoding algorithms for low-density parity-check (LDPC) codes. The Consensus and Return residual belief propagation (C&R-RBP) algorithm reduces the number of iterations required to achieve a target decoding error rate over an AWGN channel by exploiting the availability of updated information, thereby mitigating the performance degradation caused by the greedy behavior of RBP-based algorithms and reducing error propagation. The Consensus and Delayed Return RBP algorithm (C&DR-RBP) achieves better performance in the early decoding iterations than C&R-RBP, making it particularly suitable for low-latency applications. Both proposed methods maintain the same computational complexity as the original RBP algorithm in terms of residual calculations. We also provide a formal analysis showing that the Consensus mechanism increases the probability of correct bit decisions under initial decoding conditions and in the presence of severe bit transmission errors, providing insight into the performance gains observed in the simulations. Numerical results based on the rapidly growing 5G New Radio (NR) standard, considering different code lengths, code rates, and channel models, demonstrate that both methods outperform competing RBP-based algorithms with similar overall computational complexity in terms of frame error rate (FER) and bit error rate (BER).
This letter presents an enhanced list-based residual belief propagation (L-RBP) method for decoding low-density parity-check (LDPC) codes. L-RBP reduces computational complexity by scheduling a concise list of residuals. Moreover, the list is partially renewed to deter a small cluster of residuals from monopolizing renewal opportunities. Simultaneously, we also incorporate a decay mechanism to constrain the residuals retained within the list, further mitigating the greediness of the algorithm. The numerical results indicate that the L-RBP has an attractive convergence speed, error rate performance, and complexity of long-length and low-rate codes in the additive white Gaussian noise (AWGN) channel.
Low-density parity-check (LDPC) codes are favorable in modern telecommunication technologies due to its superior error-correction capability especially when the codeword length is large. The commonly-used LDPC decoders are based on the belief-propagation (BP) algorithms. It is well known that the layered (serial) belief-propagation (LBP) decoding algorithms can reduce the number of iterations by half in comparison with the flooding (parallel) BP decoding algorithms. Further reduction in total number of iterations can be achieved by using the informed dynamic scheduling techniques, such as residual BP (RBP) and node-wise residual BP (NWRBP) methods. However, the incurred additional computation of residuals is far from trivial. In this paper, we propose a novel efficient dynamic scheduling scheme, called a posteriori probability RBP (APPRBP) algorithm, which offers more flexibility to leverage the performance-complexity trade-off using a threshold parameter. The simulation results demonstrate that the average iteration numbers for our proposed APPRBP algorithm can be remarkably reduced especially in the low E_b/N_0 (signal-energy-per-information-bit to noise-power-spectral-density ratio) conditions while the bit-error rate (BER) performance is subject to slight degradation.
Low-density parity-check (LDPC) codes are favorable in modern telecommunication technologies due to its superior error-correction capability especially when the codeword length is large. The commonly-used LDPC decoders are based on the belief-propagation (BP) algorithms. It is well known that the layered (serial) belief-propagation (LBP) decoding algorithms can reduce the number of iterations by half in comparison with the flooding (parallel) BP decoding algorithms. Further reduction in total number of iterations can be achieved by using the informed dynamic scheduling techniques, such as residual BP (RBP) and node-wise residual BP (NWRBP) methods. However, the incurred additional computation of residuals is far from trivial. In this paper, we propose a novel efficient dynamic scheduling scheme, called a posteriori probability RBP (APPRBP) algorithm, which offers more flexibility to leverage the performance-complexity trade-off using a threshold parameter. The simulation results demonstrate that the average iteration numbers for our proposed APPRBP algorithm can be remarkably reduced especially in the low E_b/N_0 (signal-energy-per-information-bit to noise-power-spectral-density ratio) conditions while the bit-error rate (BER) performance is subject to slight degradation.
Belief-propagation (BP) algorithm and its variants are well-established methods for iterative decoding of LDPC codes. Among them, residual belief-propagation (RBP), which is the most primitive and representative informed dynamic scheduling (IDS) strategy, can significantly accelerate the convergence speed. However, RBP decoding suffers from a poor convergence error-rate performance due to its greedy property, which is one of the challenging issues in the design of IDS strategies. To tackle this problem, a novel IDS scheme, namely residual-decaying-based residual belief-propagation (RD-RBP) algorithm, is presented in this paper. In RD-RBP, a decaying mechanism is introduced to manipulate the residuals of those check-to-variable messages, preventing the decoding resources from being unreasonably occupied by a small group of edges in the Tanner graph. The greediness is therefore alleviated and better performance of convergence error-rate is achieved. Besides, a two-stage scheduling scheme combining prior-art variable-node and variable-to-check-edge RBP (V-VCRBP) with RD-RBP, named V-VC-RD-RBP, is proposed for achieving both fast convergence speed and a low convergence error-rate. The simulation results validate the advantages of the proposed schemes.
In order to improve the error correction performance of Low-Density Parity-Check (LDPC) codes, In this paper, we propose a Reliability Profile (RP) Based Low-Complexity Dynamic Schedule, called RPD. In terms of dynamic scheduling, the new RPD method is distinct from the existing residual belief propagation (RBP) and its variations, since RPD is based on residual criterion. Reliability divides nodes message into two categories: reliable and unreliable. By using as many messages as possible from the latest available current iteration instead of the previous iteration to update unreliable messages multiple times to speed up the convergence speed and increase the total number of updates of effective nodes message, so as to improve the Bit Error Rate (BER) performance. By not updating the reliable message, the number of ineffective nodes message updates is reduced, thereby reducing the decoding complexity. Besides, the more iterations increase, the fewer calculations of these reliable nodes. Moreover, based on reliability profile, RPD has an advantage over RBP for dynamic scheduling in that the former only needs integer operations, while the latter requires float operations. Therefore, the RPD algorithm not only accelerates the convergence speed of LDPC decoding and but also improves the BER performance while reducing the complexity.The analysis and simulation results show that the RPD strategy not only retains the fast-convergence advantage of RBP, but also has a better convergence BER performance compared to that of node-wise residual belief propagation (NW RBP). Furthermore, the simulation results show that the RPD can significantly improve the convergence speed of protograph LDPC decoding.