Abstract This letter focuses on improving the error correction performance of the extended min‐sum (EMS) decoding algorithm. Introducing factor/offset modifications in the check node update process of the EMS algorithm can improve the performance. Based on this, the authors propose a novel threshold‐based modified EMS algorithm that introduces the factor/offset in a targeted manner by setting a threshold for the posterior probability. Simulation results show that an additional performance gain of the order of 0.08 dB is obtained with the proposed method without significantly increasing the complexity of the method.
Abstract This letter focuses on improving the error correction performance of the extended min‐sum (EMS) decoding algorithm. Introducing factor/offset modifications in the check node update process of the EMS algorithm can improve the performance. Based on this, the authors propose a novel threshold‐based modified EMS algorithm that introduces the factor/offset in a targeted manner by setting a threshold for the posterior probability. Simulation results show that an additional performance gain of the order of 0.08 dB is obtained with the proposed method without significantly increasing the complexity of the method.
This letter focuses on the improvement in the error correction performance of the extended min-sum (EMS) decoding algorithm. Introducing factor/offset modifications in the check node update process of the EMS algorithm can improve the performance. Based on this, we propose a novel threshold-based modified EMS algorithm that introduces the factor/offset in a targeted manner by setting a threshold for the posterior probability. Simulation results show that an additional performance gain of the order of 0.08 dB is obtained with the proposed method without significantly increasing the method’s complexity.
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.
The extended min‐sum (EMS) and improved EMS (I‐EMS) algorithms for non‐binary low‐density parity‐check codes over GF( q ) significantly reduce the decoding complexity with an acceptable performance degradation, but they suffer from high latency because of many serial computations, including a sorting process. On the other hand, the trellis‐based EMS algorithm can greatly reduce the latency, but it does not solve the complexity problem in high‐order fields ( q ≥ 64). To improve the latency problem with low‐complexity advantages, the authors propose heap‐based EMS (H‐EMS) and heap‐based I‐EMS (HI‐EMS) algorithms that are modifications of the EMS and I‐EMS algorithms, respectively. The authors also propose double H‐EMS and double HI‐EMS algorithms trading off the latency against the performance by heaping messages twice. Numerical results show that the H‐EMS algorithm has 2.74–9.52 times lower latency than the EMS algorithm with a negligible performance degradation over a wide range of code rates, whereas the HI‐EMS algorithm has 1.20–1.62 times lower latency than the I‐EMS algorithm. Furthermore, the proposed algorithms may be employed regardless of the decoding schedules.
In this paper the combined normalized and offset extended min sum (EMS) is proposed for efficient decoding of non-binary low density parity check (LDPC) codes. EMS is the approximation of the sum product algorithm for reducing the computation complexity. However there is a performance gap between EMS and SP algorithm due to this approximation. The approximate check node messages of the extended min sum are compensated by both normalized and offset factor. The normalized factor and offset factor is determined for one iteration and is kept constant for all SNRs and iterations. It will shown in bit error rate simulation of (1008, 504) LDPC code over GF (4) that combined normalized offset extended min sum has superior performance than normalized and offset extended min sum. However, it requires only extra one multiplication for each cycle.
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.
In this paper a modified Offset Min-Sum decoding algorithm for Low-Density Parity Check Codes is presented. In this modified algorithm, the offset factor in the original Offset Min-Sum algorithm is adjusted iteratively with the assistance of the check-node computation outputs of the Normalized Min-Sum algorithm. As a result, the offset factor in our modified algorithm can be calculated adaptively and more efficiently according to the previous decoding procedure, which can minimize the decoding degradation compared with the Belief Propagation decoding algorithm. The simulation results show that, compared with the original Offset Min-Sum decoding algorithm, our modified algorithm can achieve noticeable performance improvement with minor extra hardware complexity. For example, when BER is 10−5, our algorithm can achieve 0.1dB and 0.2dB decoding gain over Offset Min-Sum algorithm for regular and irregular LDPC codes respectively.