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IEEE Systems Journal

Intelligent Dynamic Scheduling-Based Extended Min-Sum LDPC Decoding Algorithm in Cyber-Physical Systems

Chi Zhang, Xiaoxi Yi, Guicai Yu

Published Jan 1, 2023• 3 citations
Publisher

Abstract

With the construction process of smart cities, cyber-physical systems (CPS) are going to become a link to connect all things with intelligence. The low-density parity check (LDPC) code is an import information encryption format in computer networks. In this article, from the perspective of LDPC code decoding algorithm scheduling strategy, we design a dynamic check node scheduling (DCNS) strategy for extended min-sum LDPC decoding in cyber-physical systems. In this strategy, the reliability of the node is checked to determine whether to update. For the un-updated variable node, it is optimized according to the results of real-time scheduling. Compared with the flooding mechanism and LBP scheduling of the usual algorithms, this proposed scheduling strategy improves the error correction performance by selecting some nodes for decoding and performing message optimization, while not significantly increasing the decoding computation. Especially, compared with the LBP, the bit error rate and frame error rate of the proposed algorithm are reduced by 48.3% and 53.2% on average in the finite domain 64F range. Compared with BP, the bit error rate and frame error rate of the proposed algorithm are reduced by 11.3% and 13.2% on average in the finite domain 64F range.

DOI
10.1109/jsyst.2023.3294612

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With the construction process of smart cities, cyber-physical systems (CPS) are going to become a link to connect all things with intelligence. The low-density parity check (LDPC) code is an import information encryption format in computer networks. In this article, from the perspective of LDPC code decoding algorithm scheduling strategy, we design a dynamic check node scheduling (DCNS) strategy for extended min-sum LDPC decoding in cyber-physical systems. In this strategy, the reliability of the node is checked to determine whether to update. For the un-updated variable node, it is optimized according to the results of real-time scheduling. Compared with the flooding mechanism and LBP scheduling of the usual algorithms, this proposed scheduling strategy improves the error correction performance by selecting some nodes for decoding and performing message optimization, while not significantly increasing the decoding computation. Especially, compared with the LBP, the bit error rate and frame error rate of the proposed algorithm are reduced by 48.3% and 53.2% on average in the finite domain 64F range. Compared with BP, the bit error rate and frame error rate of the proposed algorithm are reduced by 11.3% and 13.2% on average in the finite domain 64F range.
Recently low-density parity check (LDPC) codes have been applied in more areas, and the research of non-binary LDPC codes has become more significant. In this paper, we establish a dynamic scheduling strategy to reduce complexity of non-binary LDPC codes decoding, and choose extended min-sum algorithm as the model. The dynamic scheduling strategy is based on the idea of nodes reliability. When decoding, we select a part of check nodes to update messages in real time according to the reliability rules, and only the variable nodes getting new messages can participate in the message propagation. Compared with usual standard flooding scheduling, this dynamic scheduling strategy can reduce decoding complexity effectively. We also optimize the message of variable nodes according to reliability, which ensure that the error correction performance of decoding algorithm is not affected. Our simulations over a BPSK-AWGN channel show that this dynamic scheduling strategy can reduce complexity in non-binary LDPC codes belief propagation decoding without affecting error correction performance.
Compared to classic channel coding,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 too complex to implement,suboptimal decoders have to be employed.One of the most popular decoding algorithms of LDPC codes is belief propagation(BP) decoding.Informed Dynamic Scheduling(IDS) can provide a better BER performance,but hard to implement due to high computational complexity increased.In order to improve the convergence,a simple low-complexity sequential check-node-based scheduling strategy is proposed.A new check-node-based reliability measure is defined,which represents the degree of reliability approximately.The reliability measure is used for ordering while the actual message updates still use the exact BP equations.During an iteration,the schedule strategy finds an update sequence,which is arranged by the new defined reliability measure in ascending order.Complexity is compared among those algorithms.Mechanism why the new strategy works effective is presented.Simulation shows that the new approach significantly improves the BER performance using short-length block LDPC codes and reduces iterations.
Among the belief-propagation (BP) decoding algorithms of low-density parity-check (LDPC) codes, the algorithms based on dynamic scheduling strategy show excellent performance. In this letter, we propose a variable-node-based dynamic scheduling decoding algorithm. For the proposed algorithm, the reliability of variable nodes is evaluated based on the log-likelihood ratio (LLR) values and the parity-check equations; then, a more accurate dynamic selection strategy is presented. Simultaneously, the oscillating variable nodes are processed so that the influence of the spread of error messages caused by oscillation are suppressed. In addition, the proposed algorithm updates the same number of messages in one iteration as the original BP decoding algorithm does, which is different from some other dynamic decoding algorithms. Simulation results demonstrate that the proposed algorithm outperforms other algorithms.
Low Density Parity Check (LDPC) codes have been widely applied in recent years, and Extended Min-Sum (EMS) decoding algorithm is the most practical algorithm, which has a fairly low computational cost. Due to the great loss in error correction performance of EMS algorithm, in this paper, we establish constraints to obtain reliable nodes while decoding and evaluate the reliability of the nodes. The nodes and information transferred between nodes are processed and optimized according to the reliability of the nodes. High reliability nodes will not be updated in the decoding process while the information of the sub-reliability nodes will be optimized in different situations, thereby improving the decoding accuracy. This algorithm can accelerate the convergence of the algorithm, while the reduced number of update nodes can control the increase of the computation to a certain extent, and maintain the advantage of the low computation quantity of EMS algorithm. Through simulation results and computational analysis, we prove that the improved algorithm has significantly improved error correction performance compared with the traditional EMS algorithm. Under the same conditions, it has completely entered the waterfall area at 3.6dB, and the EMS algorithm has not entered the waterfall area. By comparing the average iteration times of decoding of the two algorithms, the convergence speed of the algorithm can be reflected. Compared with EMS algorithm, the improved algorithm has significantly improved the convergence speed in most areas, which indicates that the processing of sub-reliable nodes accelerates the convergence of the algorithm. Finally, the average update times of the check nodes and variable nodes of the two algorithms are compared respectively. Although the improved algorithm introduces extra processing flow, it speeds up the convergence of the algorithm, and the computational cost of decoding is less expensive.
Belief propagation (BP) decoding of low-density parity-check (LDPC) codes with various dynamic decoding schedules have been proposed to improve the efficiency of the conventional flooding schedule. As the ultimate goal of an ideal LDPC code decoder is to have correct bit decisions, a dynamic decoding schedule should be variable node (VN)-centric and be able to find the VNs with probable incorrect decisions and having a good chance to be corrected if chosen for update. We propose a novel and effective metric called conditional innovation (CI) which serves this design goal well. To make the most of dynamic scheduling which produces high-reliability bit decisions, we limit our search for the candidate VNs to those related to the latest updated nodes only. Based on the CI metric and the new search guideline separately or in combination, we develop several highly efficient decoding schedules. To reduce decoding latency, we introduce multi-edge updating versions which offer extra latency-performance tradeoffs. Numerical results show that both single-edge and multi-edge algorithms provide better decoding performance against most dynamic schedules and the CI-based algorithms are particularly impressive at the first few decoding iterations.
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.