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DEStech Transactions on Computer Science and Engineering

An Adaptive Method to Improve the Iteration Efficiency for Non-binary LDPC Decoding

Jin Xu, Jun Xu, Hai Tian, Jia-hui MENG, Danfeng Zhao

Published May 5, 2017• 0 citations
Publisher

Abstract

Non-binary low density parity check codes can achieve better err-correcting performance than binary LDPC codes when the code length is moderate at the cost of higher decoding complexity. Min-Max decoding algorithm is one of the low-complexity quasi-optimal iterative algorithms. However, a problem of the Min-Max decoding algorithm is iteration inefficient in the case of low SNR. In this paper, an adaptive method is proposed based on the Min-Max decoding algorithm. By comparing the correlation among each iteration output, setting an appropriate threshold to determine whether ahead of the end of iteration, which makes the adaptive Min-Max decoding algorithm very attractive for practical purposes

DOI
10.12783/dtcse/cnsce2017/8907

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Non-binary low density parity check codes can achieve better err-correcting performance than binary LDPC codes when the code length is moderate at the cost of higher decoding complexity. Min-Max decoding algorithm is one of the low-complexity quasi-optimal iterative algorithms. However, a problem of the Min-Max decoding algorithm is iteration inefficient in the case of low SNR. In this paper, an adaptive method is proposed based on the Min-Max decoding algorithm. By comparing the correlation among each iteration output, setting an appropriate threshold to determine whether ahead of the end of iteration, which makes the adaptive Min-Max decoding algorithm very attractive for practical purposes
When the code length is moderate, non-binary low-density parity-check (NB-LDPC) codes can achieve better error correcting performance than their binary counterparts at the expense of higher decoding complexity. The check node processing is a major bottleneck of NB-LDPC decoding. In this paper, Min-max decoding algorithm is proposed based on a new forward backward processing method of check nodes, select only a part of the most reliable information to the forward-backward calculation process, and change the variable nodes to check nodes (v-to-c) generation of information. Using this algorithm, a kind of code (768,1152) defined on GF(4) is simulated and compared with belief propagation in log domain (LOG-BP) decoding algorithm. Simulation results show Min-max decoding algorithm reduce information storage requirements and the computational complexity, conducive to engineering implementation.
Iterative decoding of non-binary LDPC codes is currently performed using either the sum-product or the min-sum algorithms or slightly different versions of them. In this paper, several low-complexity quasi-optimal iterative algorithms are proposed for decoding non-binary codes. The min-max algorithm is one of them and it has the benefit of two possible LLR domain implementations: a standard implementation, whose complexity scales as the square of the Galois field's cardinality and a reduced complexity implementation called selective implementation, which makes the min-max decoding very attractive for practical purposes.
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 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.
Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than binary LDPC codes when the code length is moderate. For the first time, this paper proposes a partial-parallel decoder architecture based on the Min-max algorithm for quasi-cyclic NB-LDPC codes. A novel boundary tracking based scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In addition, layered decoding is applied, and the hardware units are optimized to reduce the latency and area. This paper also introduces an overlapped method for the check node processing among different layers to further speed up the decoding. From complexity analysis, the proposed decoder with 5 iterations for a (837,726) code over GF(25) can easily achieve 60 Mbps throughput on ASIC devices. It is 40% more efficient than prior designs.