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IEEE International Conference on High Performance Computing and Communications; IEEE International Conference on Smart City; IEEE International Conference on Data Science and Systems (HPCC/SmartCity/DSS)

Weighting Factors Optimization for NB-LDPC Codes Based on Extended Min-Sum Algorithm

Mingjuan Qiu, Ming Zhan, Liangxi Liu, Yi Deng, Xiaohong Luo

Published Dec 1, 2020• 0 citations
Publisher

Abstract

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).

DOI
10.1109/hpcc-smartcity-dss50907.2020.00110

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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).
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).
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.
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.
Low Density Parity Check (LDPC) codes over a Galois Field GF(q) can provide significantly better error- correcting quality than binary LDPC codes with moderate code length. However, the computational complexity and memory requirement of nonbinary codes are much higher, limiting the application of non- binary LDPC codes. In this paper, we propose an adaptive message truncation algorithm for non-binary LDPC decoding, guided by the estimated code error rates. Compared to the previous fixed message truncation method, it can cut the messages adaptively, and therefore provide better decoding quality and computation complexity reduction. To further reduce the computation, we propose another adaptive check node update algorithm, simplifying the decoding by reducing the number of check nodes updating. Our simulation results demonstrate that by combining these two algorithms together, the average message size can be reduced greatly and good decoding quality is achieved, at a little cost of iterations. Compared to the existing truncation algorithms, our approach can reduce the order of complexity to O(nalog2(na)) (where nais messages size), with less performance degradation.
The extended min-sum (EMS) algorithm for decoding low-density parity-check codes over the finite field with q elements significantly reduces decoding complexity by truncating each message of length q into a message of effective length nm. The number of effectively dominant components in each truncated message may gradually decrease with the number of decoding iterations. Based on this observation, we propose a novel adaptive EMS algorithm, called a two-length EMS (TL-EMS) algorithm. It chooses one of two candidate values as the effective message length nmfor each message by reflecting the concept called message separation. Numerical results show that it can significantly reduce the computational complexity with little performance degradation.
In this paper, we proposed a modified Trellis extended min-sum (T-EMS) algorithm with L truncations for non-binary low density parity check (NB-LDPC) codes. The proposed algorithm achieves to reduce complexity of T-EMS algorithm, especially on large order Galois fields GF(q). In order to improve the error-correcting performance of the algorithm, an elitist selection (ES) strategy is presented, which enlarges the belief value of the selected symbols. As a proof, the simulation results and complexity analysis show that with the increase of q, the complexity decreases obviously. However, in the case of a suitable L value, the LT-EMS algorithm with ES strategy is not inferior to the T-EMS algorithm in performance. In addition, the ES strategy can accelerate the convergence rate and reduce the number of iterations of the decoding process, which will enhance the decoding throughput.