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IEEE International Conference on Acoustics Speech and Signal Processing

Nonbinary LDPC decoding by min-sum with Adaptive Message Control

Weiguo Tang, Jie Huang, Lei Wang, Shengli Zhou

Published May 1, 2011• 8 citations
Publisher

Abstract

A new decoding algorithm, referred to as Min-Sum with Adaptive Message Control (AMC-MS), is proposed to reduce the decoding complexity of nonbinary LDPC codes. The proposed algorithm adaptively trims the message length of belief information to reduce the amount of arithmetic operations. Exploiting the fact that during the decoding iteration, the distribution of belief information will become more concentrated around the correct element in the case of convergence, the messages can be truncated accordingly by considering only a few entries with large likelihood. Simulation results with a GF(16) nonbinary LDPC code indicate that the proposed approach can reduce arithmetic operations by up to 65% compared with non-truncated cases. Compared with the state-of-the-art extended MS (EMS) decoding, the proposed AMC-MS algorithm can reduce the computation by up to 50%, thereby enabling low-complexity decoding of nonbinary LDPC codes.

DOI
10.1109/icassp.2011.5946693

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A new decoding algorithm, referred to as Min-Sum with Adaptive Message Control (AMC-MS), is proposed to reduce the decoding complexity of nonbinary LDPC codes. The proposed algorithm adaptively trims the message length of belief information to reduce the amount of arithmetic operations. Exploiting the fact that during the decoding iteration, the distribution of belief information will become more concentrated around the correct element in the case of convergence, the messages can be truncated accordingly by considering only a few entries with large likelihood. Simulation results with a GF(16) nonbinary LDPC code indicate that the proposed approach can reduce arithmetic operations by up to 65% compared with non-truncated cases. Compared with the state-of-the-art extended MS (EMS) decoding, the proposed AMC-MS algorithm can reduce the computation by up to 50%, thereby enabling low-complexity decoding of nonbinary LDPC codes.
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.
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.
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.
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.
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).
We propose a low-complexity decoding message truncation technique for nonbinary LDPC decoders by exploiting the extended min-sum algorithm. The proposed technique dynamically adjusts the decoding message length according to channel conditions, thereby reducing the decoding complexity while conforming to the desired level of decoding performance. Utilizing the proposed technique, the decoding operations as well as the power consumption of the non-binary LDPC decoder can be greatly reduced. Simulation results demonstrate that the proposed technique can achieve a better power-performance tradeoff over conventional techniques.