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IEEE Asia-Pacific Conference on Antennas and Propagation

Modified EMS Decoding Algorithm Combined with Feedback Theory

Fang Ye, Ruo-Lin Wang, Qian Sun

Published Aug 1, 2018• 0 citations
Publisher

Abstract

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.

DOI
10.1109/apcap.2018.8538227

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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.
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 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).
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).
This letter is concerned with low-complexity decoding algorithms for nonbinary low-density parity-check (NB-LDPC) codes. A new truncation rule based on an adaptive threshold μ is proposed for the extended min-sum (EMS) algorithm. The threshold μ is determined by the mean of the message vector. Therefore, it can be matched to channel observation and decoding iteration. The resulting algorithm is referred to as μ-EMS algorithm. Simulation results show that the μ-EMS algorithm performs almost as well as the Q-ary sum-product algorithm (QSPA). Simulation results also show that the μ-EMS algorithm is simpler than the other X-EMS algorithms for NB-LDPC over high order finite fields.
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.
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.