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Dianzi xuebao

Decoding Algorithm for Non-Binary LDPC Codes Based on Node-Subset and k-Order Message Truncation

Youming Sun, Haiqiang Chen, Xiangcheng Li, Wan Haibin, Zuo Tuanfa

Published Jan 1, 2017• 1 citation
OpenAlex

Abstract

This paper presents a low complexity non-binary LDPC decoding algorithm,whose complexity can be reduced in the following two ways.First,a new truncation scheme is presented to define the processing/non-processing check node subsets.The check nodes with relatively high reliability are not required to be processed,which can reduce the complexity.Second,for the check nodes in the processing subset,we further present a k-order message truncation for the states and branches of the check node Trellis.In the decoding iterations,only those live states/branches are involved in the message updating process,which can further reduce the computational loads at check nodes.Simulation results show that the presented algorithm performs very closely to several existing improved EMS decoding algorithms,but it has the lowest complexity when decoding the non-binary LDPC codes constructed both in low/high order fields.%

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This paper presents a low complexity non-binary LDPC decoding algorithm,whose complexity can be reduced in the following two ways.First,a new truncation scheme is presented to define the processing/non-processing check node subsets.The check nodes with relatively high reliability are not required to be processed,which can reduce the complexity.Second,for the check nodes in the processing subset,we further present a k-order message truncation for the states and branches of the check node Trellis.In the decoding iterations,only those live states/branches are involved in the message updating process,which can further reduce the computational loads at check nodes.Simulation results show that the presented algorithm performs very closely to several existing improved EMS decoding algorithms,but it has the lowest complexity when decoding the non-binary LDPC codes constructed both in low/high order fields.%
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).
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.
Non-binary low-density parity-check (NB-LDPC) codes outperform their binary counterparts in some cases, but their high decoding complexity is a significant hurdle to their applications. In this paper, we propose a decoding algorithm with reduced computational complexities and smaller memory requirements for NB-LDPC codes over large fields. First, a simplified algorithm is proposed to reduce the computational complexity of variable node processing. To reduce memory requirements, existing NB-LDPC decoders often truncate the message vectors to a limited number nmof values. However, the memory requirements of these decoders remain high when the field size is large, since nmneeds to be large enough to alleviate error performance degradation. In this paper, an improved trellised based check node processing algorithm is proposed to significantly reduce the memory requirement. The number of elements in a variable-to-check message is reduced to nv(nvm). The sorted log likelihood ratio (LLR) vector of a check-to-variable message is approximated using a piece-wise linear function. Thus, only few LLRs are stored and other LLRs are computed on-the-fly when needed. For each a priori message, most LLRs are approximated with a linear function. Our numerical results demonstrate that the proposed decoding algorithm outperforms existing algorithms. Two LLR generation units (LGUs) are proposed to compute LLR vectors for check-to-variable messages, and the two LGUs require only a fraction of the area needed to store nmLLRs.
In this paper, we propose a new implementation of the Extended Min-Sum (EMS) decoder for non-binary LDPC codes. A particularity of the new algorithm is that it takes into accounts the memory problem of the non-binary LDPC decoders, together with a significant complexity reduction per decoding iteration. The key feature of our decoder is to truncate the vector messages of the decoder to a limited number nmof values in order to reduce the memory requirements. Using the truncated messages, we propose an efficient implementation of the EMS decoder which reduces the order of complexity to ¿(nmlog2nm). This complexity starts to be reasonable enough to compete with binary decoders. The performance of the low complexity algorithm with proper compensation is quite good with respect to the important complexity reduction, which is shown both with a simulated density evolution approach and actual simulations.
In this paper, we use a column-wise, row-wise approach for efficiently choosing reliable messages in decoding non-binary Low-Density Parity-Check (LDPC) codes, and build configurations with those reliable messages for updating check nodes. This method decreases the number of configurations compared to conventional trellis-based decoding algorithms. In addition, a novel algorithm with precomputed messages is proposed which improves decoding performance. Using the reduced configuration set with the improved message updating scheme it is shown that we can achieve an improved decoding performance while reducing the hardware complexity. Compared to trellis-based decoders, the proposed decoder reduces the number of required operations in computing check-to-variable messages and achieves better error-correcting performance.
In this paper, we propose a new improved algorithm to reduce the decoding complexity of NB-LDPC codes especially when the number of iteration is large. The proposed algorithm is based on the extended min-sum (EMS) which truncates the message vectors and trellis-based EMS (T-EMS) which employs the trellis representation. Our modification of EMS introduces the thresholds to further truncate the incoming messages to the check node. The performance of our improved new algorithm is only 0.05dB (resp 0.2dB) to BP in the waterfall region over GF(8) (resp GF(128)), but the complexity will reduce to lower than half of the EMS when the threshold is chosen reasonable.