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International Wireless Communications and Mobile Computing Conference (IWCMC)

Genie-aided adaptive normalized min-sum algorithm for LDPC decoding

Yue Liu, Kewu Peng, Changyong Pan, Liwen Fan

Published Aug 1, 2015• 8 citations
Publisher

Abstract

This paper proposes an algorithm for the decoding of low-density parity check (LDPC) codes, aiming to retrieve the performance degradation of conventional normalized min-sum algorithm, especially for irregular LDPC code. In our proposed algorithm, normalization factors are adjusted dynamically and adaptively during iterative decoding process according to look-up tables obtained by training and simulation in our proposal. The look-up tables construct the relationship between normalization factor a and the failed parity-check equation proportion p, which could be calculated in each decoding process. Simulation results demonstrate that the proposed algorithm can achieve a performance closer to the sum-product algorithm and a coding gain of around 0.2dB compared to the conventional normalized min-sum algorithm for rate 2/3 irregular LDPC codes over the AWGN channel. Our proposal is independent from the channel characteristics and retains low complexity. The implementation facility and the excellent performance make the proposed algorithm expect a wide application.

DOI
10.1109/iwcmc.2015.7289086

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This paper proposes an algorithm for the decoding of low-density parity check (LDPC) codes, aiming to retrieve the performance degradation of conventional normalized min-sum algorithm, especially for irregular LDPC code. In our proposed algorithm, normalization factors are adjusted dynamically and adaptively during iterative decoding process according to look-up tables obtained by training and simulation in our proposal. The look-up tables construct the relationship between normalization factor a and the failed parity-check equation proportion p, which could be calculated in each decoding process. Simulation results demonstrate that the proposed algorithm can achieve a performance closer to the sum-product algorithm and a coding gain of around 0.2dB compared to the conventional normalized min-sum algorithm for rate 2/3 irregular LDPC codes over the AWGN channel. Our proposal is independent from the channel characteristics and retains low complexity. The implementation facility and the excellent performance make the proposed algorithm expect a wide application.
This paper proposes an adaptive normalized min-sum algorithm for the decoding of low-density parity check (LDPC) codes, which utilizes an adaptive normalization factor to improve the accuracy of the soft information transferred during the iterative decoding process, and provides superior performance accordingly. This adaptive normalization factor can be adjusted dynamically and adaptively at each decoding iteration according to a look-up table obtained via training and simulation. Its implementation facility and independence from the channel characteristics make the proposed adaptive normalized min-sum algorithm expect a wide application. Simulation results show that the proposed algorithm can achieve performance much closer to the sum-product algorithm and a coding gain of around 0.2dB compared to the conventional normalized min-sum algorithm for DVB-S2's rate 2/5 and 3/5 LDPC codes over the additive white Gaussian noise (AWGN) channel.
In this paper a modified Offset Min-Sum decoding algorithm for Low-Density Parity Check Codes is presented. In this modified algorithm, the offset factor in the original Offset Min-Sum algorithm is adjusted iteratively with the assistance of the check-node computation outputs of the Normalized Min-Sum algorithm. As a result, the offset factor in our modified algorithm can be calculated adaptively and more efficiently according to the previous decoding procedure, which can minimize the decoding degradation compared with the Belief Propagation decoding algorithm. The simulation results show that, compared with the original Offset Min-Sum decoding algorithm, our modified algorithm can achieve noticeable performance improvement with minor extra hardware complexity. For example, when BER is 10−5, our algorithm can achieve 0.1dB and 0.2dB decoding gain over Offset Min-Sum algorithm for regular and irregular LDPC codes respectively.
In this paper, a modified normalized Min-Sum algorithm (MNMSA) is proposed for decoding irregular Low Density Parity Check Codes (LDPC) with non-uniform degree distribution. The proposed algorithm provides an efficient decoding scheme to enhance the error performance of an irregular LDPC code without increasing the hardware complexity. An efficient 6- bit quantization scheme is utilized in the proposed algorithm with optimally combined normalization and down scaling factors to resolve the magnitude overestimation issue which occurs during iterative message passing process between the nodes. The simulation results demonstrate that the proposed algorithm achieves good decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without the requirement of complex arithmetic calculations. Compared to other min- sum based decoding algorithms the decoding process of the proposed MNMSA requires only fewer decoding iterations over wide range of signal- to- noise ratio (SNR) to achieve comparable decoding performance to that of Belief Propagation (BP) algorithm without increasing the hardware complexity.
Offset Min-Sum Algorithm (OMSA) and Normalized Min-Sum Algorithm (NMSA) are widely used in commercial LDPC decoders due to low complexity and reasonable performance. In this paper we proposes an Adaptive Layered Offset min- sum algorithm for the decoding of LDPC codes, which utilizes an adaptive offset factor to improve the accuracy of the soft information transferred during the iterative decoding process, and it provides good performance accordingly. The performed simulations showed that the layered offset min-sum decoding for LDPC codes can provide significant improvement compared to existing MS based algorithm, OMSA and NMSA.
This paper analyzes the performance of quantized min-sum decoding algorithms for irregular low-density parity-check (LDPC) codes. For regular LDPC codes, it is known that the normalized or offset min-sum decoding algorithm with quantization bits less than 6 bits achieves good performances over wide range of signal-to-noise ratios (SNR). However, finite precision effects in decoding irregular LDPC codes are different from that in decoding regular LDPC codes which is caused by the difference of convergence speeds between low degree nodes and high degree nodes. This paper proposes a novel method to improve the performance of the conventional normalized or offset min-sum decoding algorithm when it is approximated with finite precision for hardware implementations. The proposed method applies down-scaling factors to intrinsic information which has effects on increasing the reliability of extrinsic information at variable nodes and compensating the quantization errors caused by finite precision. Computer simulation results for irregular LDPC codes show that the proposed normalized and offset min-sum decoding algorithms achieve better performances at high SNR compared to the conventional normalized and offset min-sum algorithms under (6:2) quantization scheme.