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Modified Normalized Min-Sum decoding of LDPC codes

Rong Chen, Yiming Wang

Published Oct 1, 2008• 3 citations
Publisher

Abstract

In this paper, we present an improvement on the normalized min-sum (NMS) decoding algorithm for low density parity check codes. The modified NMS (M-NMS) algorithm introduces a more efficient adjustment for check node update computation. Taking the sub-minimum value among extrinsic information from the variable nodes into consideration, we make the correction factor varies with different iterations. Results show that, compared with standard min-sum (MS) and NMS decoding algorithms, the proposed method not only offers a better performance but also achieves a lower error floor in the high SNR region.

DOI
10.1109/icosp.2008.4697491

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In this paper, we present an improvement on the normalized min-sum (NMS) decoding algorithm for low density parity check codes. The modified NMS (M-NMS) algorithm introduces a more efficient adjustment for check node update computation. Taking the sub-minimum value among extrinsic information from the variable nodes into consideration, we make the correction factor varies with different iterations. Results show that, compared with standard min-sum (MS) and NMS decoding algorithms, the proposed method not only offers a better performance but also achieves a lower error floor in the high SNR region.
Low-density parity-check code (LDPC) is a kind of better error correction code which is played an important role in the reliability transmission of communication systems. In the aspect of decoding algorithm, the NMS algorithm becomes the mainstream algorithm dues to its lower complexity. what’s more, the Semi-serial decoding algorithm was put forward to reduce decoding iterations. However, the compensation factor of NMS algorithm is a fixed value and the Semi-serial decoding algorithm only considers one aspect of reducing iterations. In the actual decoding process, this value varies with the degree of the check node and the number of iterations. in order to solve the problems of these algorithms, this paper will propose a new improved algorithm. Firstly, we will adopt a dynamic compensation factor to improve performance of NMS algorithm on regular LDPC code. Then combined with the idea of Semi-serial decoding algorithm to reduce the number of iterations. The dynamic factor is firstly analyzed theoretically by density evolution theory. Then through the Monte Carlo experiment and the true LLR, the suitable dynamic compensation factors can be obtained which is changes with the number of iterations.
In this work, we propose a neural adjusted min-sum (NAMS) decoder for low-density parity-check (LDPC) codes. In particular, we improve the traditional normalized min-sum (NMS) decoder by introducing a selection mechanism to adjust the check-node update step, where either the min-sum rule or the belief propagation (BP) rule is selected. Besides, we unfold the modified decoder into a model-driven neural network, where layer-dependent trainable parameters are introduced as weights in the Tanner graph and optimized by gradient descent-based methods during network training. Simulation results demonstrate that the proposed NAMS decoder is able to provide superior error-correction performance as compared to the neural NMS decoder, with only slightly increased computational complexity. Moreover, in certain circumstances, the proposed NAMS decoder even outperforms the neural BP decoder, with much lower computational complexity.
This paper proposes a low-complexity LDPC decoding algorithm with simplified check nodes updating. The proposed algorithm simplifies the result of the second-minimum in check nodes based on the first-minimum computation instead of computing it directly. In order to obtain the approximate result, effective corrected coefficients are utilized, which can reduce the complexity by eliminating the complex computations. Complexity analysis is provided and the results indicate that the complexity of the proposed algorithm is much lower than the general NMS algorithm and MS-based simplified algorithms. Simulation results show that the performance of the proposed algorithm can closely match the NMS algorithm with the same number of iterations.
A hybrid decoding algorithm for low-density parity-check codes is presented. The proposed algorithm applies different updating schemes, such as the normalized min-sum (NMS) simplification and linear approximation, to the check-node based on its degree. Meanwhile, to eliminate the dependence on the channel variance estimation, the proposed algorithm adopts a multiplicative factor to initialize the channel input and a fixed linear functions for check-node updating. From the iterative thresholds and decoding simulations, our proposed algorithm can be shown to achieve improved performance (much closer to that of the belief propagation decoding) at the expense of a slight increase in complexity to NMS algorithm.