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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Reliability-List-Based Check-Belief Propagation Decoding of LDPC Codes

Zhe Liu, Wu Guan, Ziqin Yan, Liping Liang

Published Dec 18, 2024• 1 citation
Publisher

Abstract

Reliability-based belief propagation (RBP) decoding algorithms are used to decode low-density parity-check (LDPC) codes. However, due to the reliability of comparing and sorting in traditional algorithms, conventional RBP decoders significantly lose in resource consumption. This letter presents an enhanced reliability list-based check-belief propagation (RL-CBP) algorithm. The RL-CBP algorithm reduces computational complexity by scheduling a concise list of check-beliefs. Moreover, the list is applied for comparisons and selections of check-beliefs. The selected check-belief transforms the decoding message between edges; all check-beliefs are iteratively enlarged according to the reliabilities, and high-performance decoding will be achieved. The simulation results and analyses show that the proposed method achieves a reliability-list gain compared with the check-belief propagation (CBP) algorithm but consumes much fewer calculations than the traditional RBP algorithm.

DOI
10.1587/transfun.2024eal2080

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Reliability-based belief propagation (RBP) decoding algorithms are used to decode low-density parity-check (LDPC) codes. However, due to the reliability of comparing and sorting in traditional algorithms, conventional RBP decoders significantly lose in resource consumption. This letter presents an enhanced reliability list-based check-belief propagation (RL-CBP) algorithm. The RL-CBP algorithm reduces computational complexity by scheduling a concise list of check-beliefs. Moreover, the list is applied for comparisons and selections of check-beliefs. The selected check-belief transforms the decoding message between edges; all check-beliefs are iteratively enlarged according to the reliabilities, and high-performance decoding will be achieved. The simulation results and analyses show that the proposed method achieves a reliability-list gain compared with the check-belief propagation (CBP) algorithm but consumes much fewer calculations than the traditional RBP algorithm.
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.
Variant belief propagation (BP) algorithms are applied to low-density parity-check (LDPC) codes. However, conventional decoders suffer from a large resource consumption due to gathering messages from all the neighbour variable-nodes and/or check-nodes through cumulative calculations. In this paper, a check-belief propagation (CBP) decoding algorithm is proposed. Check-belief is used as the probability that the corresponding parity-check is satisfied. All check-beliefs are iteratively enlarged in a sequential recursive order, and successful decoding will be achieved after the check-beliefs are all big enough. Compared to previous algorithms employing a large number of cumulative calculations to gather all the neighbour messages, CBP decoding can renew each check-belief by propagating it from one check-node to another through only one variable-node, resulting in a low complexity decoding with no cumulative calculations. The simulation results and analyses show that the CBP algorithm provides little error-rate performance loss in contrast with the previous BP algorithms, but consumes much fewer calculations and memories than them. It earns a big benefit in terms of complexity.
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.
Reliability-Based-Layered Belief Propagation (RBL-BP) decoding algorithm for LDPC codes is proposed in this paper. Being an informed dynamic schedule (IDS), it measures convergence and selects iterations by the absolute value of logarithmic likelihood ratio information obtained from channel (ABS-LLR-CH). Each variable node can select its own iterations by estimating its own convergence, and finish iterative decoding. Simulation results show that the proposed RBL-BP algorithm has better performance than those of flooding schedule, layered belief propagation (LBP) and variable-to-check residual belief propagation (VC-RBP). For the convergence property of IDS, the proposed algorithm has faster speed than those of flooding schedule and LBP with a little increase in complexity while it has almost no speed decrease with much lower computational complexity than VC-RBP.
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 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.