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Mediterranean Microwave Symposium

Decoding of iterative Non-Binary LDPC codes using a near Maximum Likelihood approach

Ali Chamas Al Ghouwayel, Abdel-karim Ajami, Hussein Hijazi

Published Sep 1, 2013• 0 citations
Publisher

Abstract

This paper investigates the decoding of rate 1/2 Non-Binary LDPC codes using a non-iterative approach based on the Maximum-Likelihood (ML) principle. The iterative decoding approach based on the well known Extended-Min-Sum (EMS) algorithm, considered as the most efficient decoding algorithm to decode NB-LDPC codes, executes the decoding process iteratively. The main operations of this algorithm are the variable and check node updates which are performed at least eight times requiring a long decoding time to achieve good performance in terms of Frame Error Rate (FER). The proposed decoding near ML approach is based on ML search where the number of candidates is highly reduced using a technique privileging the most reliable and nearest codewords. Simulation results show that the proposed algorithm achieves, at a reduced list of 5 searched candidates in average at 3 dB, the performance offered by the EMS algorithm. We also show that by slightly increasing the list of candidates, the proposed algorithm outperforms the EMS algorithm.

DOI
10.1109/mms.2013.6663104

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This paper investigates the decoding of rate 1/2 Non-Binary LDPC codes using a non-iterative approach based on the Maximum-Likelihood (ML) principle. The iterative decoding approach based on the well known Extended-Min-Sum (EMS) algorithm, considered as the most efficient decoding algorithm to decode NB-LDPC codes, executes the decoding process iteratively. The main operations of this algorithm are the variable and check node updates which are performed at least eight times requiring a long decoding time to achieve good performance in terms of Frame Error Rate (FER). The proposed decoding near ML approach is based on ML search where the number of candidates is highly reduced using a technique privileging the most reliable and nearest codewords. Simulation results show that the proposed algorithm achieves, at a reduced list of 5 searched candidates in average at 3 dB, the performance offered by the EMS algorithm. We also show that by slightly increasing the list of candidates, the proposed algorithm outperforms the EMS algorithm.
In this paper, we investigate the decoding of short Non-Binary (NB)-LDPC codes of rate 1/2 using a non-iterative approach based on the Maximum-Likelihood (ML) principle. The traditional decoding algorithms used to decode the NB-LDPC codes are by nature iterative where the Variables Nodes (VN) and Check Nodes (CN) exchange data iteratively during, at least, eight iterations which imposes a long decoding time to achieve good performance in terms of Frame Error Rate (FER). In this paper we propose a decoding algorithm based on the Maximum Likelihood (ML) search named Near ML approach where the number of tested words considered as potential codewords is highly reduced. Simulation of codes of lengths 16 and 48 are presented and the results show that the proposed algorithm achieves the performance offered by the EMS algorithm. The NB-LDPC of length 16 is shown to outperform the EMS algorithm.
This paper presents an improved decoding algorithm of non-binary LDPC codes based on the Expanded Min-Sum algorithm,analyzes the complexity of the algorithm in decoding efficiency.According to the fact that the reliability of variable note is increased with the increase of the iterative number,the reliability of the variable notes is estimated by the maximum post probability of variable notes and illegal parity-check values.By the estimation rule,the iterative calculations or some variable notes are stopped,the number of calculation for updating variable and parity-check notes is reduced,thus the decoding complexity is decreased and the decoding efficiency is improved.A simulation is made using regular non-binary LDPC codes under White Gaussian Noise channel based on GF(4),the result shows that the performance decreases by about 0.05 dB when BER(Bit Error Rate) is,but the decoding complexity is reduced and the decoding efficiency is improved significantly.
The extended min-sum algorithm (EMS) for decoding non-binary low density parity check (NB-LDPC) codes reduces the decoding complexity by truncating the message vector by retaining only the most reliable symbols. However, the EMS algorithm does not consider that the noise of the received codeword is gradually reduced as the iteration count goes up. In this paper, we propose a low-complexity adaptive EMS algorithm, called threshold-based EMS (TB-EMS). The TB-EMS algorithm has a simple adaptive rule to calculate the new message vector length compared to the A-EMS. The proposed algorithm selects one of two message vector lengths. Experimental results show that the proposed algorithm reduces the decoding complexity with minimal performance degradation compared with the EMS algorithm. Further, the decoding performance of the TB-EMS is better than A-EMS.
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.
Non-binary low-density parity-check (NB-LDPC) codes are an extension of binary LDPC codes with significantly better performance when the code length is moderate. Previously, forward-backward schemes are used to implement check node processing, which need large memory. In this paper, a novel approach is proposed for EMS NB-LDPC decoding. Compared to EMS decoding algorithm, the message memory and the average number of iterations have been reduced. Also, the overall decoder architecture is proposed.
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).