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IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (APWC)

Improved Extended Min-Sum Algorithm for Non-Binary LDPC Codes Based on Node Reliability

Yibing Li, Sitong Zhang, Fang Ye, Yaqiang Zhou, Ye Tian, Tao Jiang

Published Sep 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1109/apwc.2019.8870565

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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.
In comparison to the binary LDPC codes, the nonbinary low-density parity-check (NB-LDPC) codes have the advantage of solving burst errors. In order to improve the accuracy of the decoding results, an improved extended min-sum (EMS) algorithm is proposed in this paper. By adopting the feedback idea of joint iterative detection algorithm and introducing the reliability and stability parameters, the new algorithm can mitigate the influence of Log-likelihood ratio (LLR) oscillation on the decoding result and adjust the update information of the check node properly, thereby improving the decoding accuracy. This method can effectively restrain the LLR oscillation and speed up the convergence rate, thus the final decision result can be amended. Simulation results show that, the proposed improved EMS decoding algorithm heightens the bit error rate performance and reduces average number of iterations, meanwhile the additional computations are within acceptable range.
The extended min-sum (EMS) algorithm is adopted for non-binary low density parity check (NB-LDPC) codes. The high complexity of EMS algorithm is a hot topic in recent years. Aiming at the problem, a low-complexity EMS algorithm based on NB-LDPC codes is proposed. Dynamic bubble-check (DBC) algorithm in elementary check node (ECN) steps is adopted to reduce the complexity of check node. Furthermore, the proposed algorithm dynamically truncates the length of the message vector by the number of decoding iterations. Taking the length of message vector truncated again as half of the original one as an example, the simulation results and complexity are analyzed. Analysis shows that, compared to the EMS algorithm, computational complexity of comparisons and real additions of check node of the proposed algorithm have reduced by about 70% and 25% respectively. Meantime, the decoding performance of the proposed algorithm approach that of EMS algorithm and the loss is only near 0.08 dB when the bit error rate (BER) is 10−3and the Galois fieldGF(q)(q=16)GF(q)(q=16)GF(q)(q=16).
Although non-binary low-density parity-check (NB-LDPC) codes have better error-correction capability than that of binary LDPC codes, their decoding complexity is significantly higher.Therefore, it is crucial to reduce the decoding complexity of NB-LDPC while maintaining their error-correction capability to adopt them for various applications.The extended min-sum (EMS) algorithm is widely used for decoding NB-LDPC codes, and it reduces the complexity of check node (CN) operations via message truncation.Herein, we propose a low-cost CN processing method to reduce the complexity of CN operations, which take most of the decoding time.Unlike existing studies on low complexity CN operations, the proposed method employs quick selection algorithm, thereby reducing the hardware complexity and CN operation time.The experimental results show that the proposed selection-based CN operation is more than three times faster and achieves better error-correction performance than the conventional EMS algorithm.
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The decoding algorithms of Nonbinary low-density parity-check (NB-LDPC) codes mainly include Belief Propagation (BP), Fast Fourier Transforms (FFT) and Extended Min-Sum (EMS). Among these decoding algorithms, although EMS has the lowest decoding complexity, there is still room for improvement. Therefore, this paper proposes a new algorithm based on the EMS algorithm to further improve the decoding complexity and performance. In order to reduce complexity, an adaptive truncation rule is added to the decoding process. The adaptive truncation rule chooses the length of automatic truncation to reduce the average number of iterations. Thus, the complexity of decoding algorithm is reduced. Besides the weighting factors is added to the variable update iteration process, which effectively improves the decoding performance. The results show that the proposed algorithm has about 0.9 dB gain compared with the EMS decoding algorithm when the bit error rate (BER) is 10--4and the Galois field GF(q) (q16).
To overcome the drawback of the extended min-sum algorithm(EMS),an improved EMS decoding algorithm is proposed,which is designed for LDPC over GF(q).The algorithm adaptively chooses the rank of FHT in each iteration step according to the average variance of bit nodes' probability pairs.It differs from the original EMS algorithm in which the rank of FHT for each iteration step is a constant.Moreover,for oscillating variable nodes,the message of the previous iteration is added to the current message in the iterative procedure to reduce loss of performance and effects of oscillation.Experimental results show that the proposed algorithm can achieve better performance and converge faster than EMS with the same decoding complexity.