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Modified Scaled Min Sum LDPC Decoder for DVB-S2/S2X/T2

Fady Tadros, Saleh M. Eisa, Hanady H. Issa, Khaled Shehata

Published Dec 1, 2018• 1 citation
Publisher

Abstract

Min sum algorithm (MSA) is widely used for decoding Low Density Parity Check (LDPC) codes in many modern Digital Video Broadcasting (DVB) as a simplification for Sum Product Algorithm (SPA) which greatly reduce the implementation complexity. This paper presents a design of modified variable scaling min sum LDPC decoding algorithm for DVB-S2/S2X/T2. The proposed design is a combination between the variable Normalized Min Sum Algorithm (NMSA) and the Offset Min Sum Algorithm (OMSA) which provides a trade-off between decoding complexity and error correcting performance. It improves the use of the Min Sum Algorithm (MSA) by 39%. A proposal for how to implement the proposed algorithm using FPGA is also introduced. The structure used is partially parallel layered decoder architecture.

DOI
10.1109/icm.2018.8704096

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Min sum algorithm (MSA) is widely used for decoding Low Density Parity Check (LDPC) codes in many modern Digital Video Broadcasting (DVB) as a simplification for Sum Product Algorithm (SPA) which greatly reduce the implementation complexity. This paper presents a design of modified variable scaling min sum LDPC decoding algorithm for DVB-S2/S2X/T2. The proposed design is a combination between the variable Normalized Min Sum Algorithm (NMSA) and the Offset Min Sum Algorithm (OMSA) which provides a trade-off between decoding complexity and error correcting performance. It improves the use of the Min Sum Algorithm (MSA) by 39%. A proposal for how to implement the proposed algorithm using FPGA is also introduced. The structure used is partially parallel layered decoder architecture.
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It is well known that for decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs). In this paper, we demonstrate that, for quantized LDPC decoders, although the MSA achieves better high SNR performance than the AMSA and OMSA, each of the MSA, AMSA, and OMSA all suffer from a relatively high error floor. Therefore, we propose a novel modification of the MSA for decoding quantized LDPC codes with the aim of lowering the error floor. Compared to the quantized MSA, the proposed modification is also helpful at low SNRs, where it matches the waterfall performance of the quantized AMSA and OMSA. The new algorithm is designed based on the assumption that trapping/absorbing sets (or other problematic graphical objects) are the major cause of the error floor for quantized LDPC decoders, and it aims to reduce the probability that these problematic objects lead to decoding errors.
Min-sum algorithm(MSA) and its modification are used in LDPC decoder implementations because of its error performance and low computation complexity. In this paper a modified min-sum LDPC decoding algorithm through approximation enhancement using the smallest three minimum values is presented. The proposed algorithm improves error performance and reduces decoder iterations. From the simulation results for 5G NR LDPC codes, we show that the proposed algorithm can achieve about 1.6dB improvement of FER compared to the min-sum decoding algorithm and provide about 10% reduction of the average iteration numbers compare to NMSA with optimum normalization factor.
To offer commercial LDPC decoders with better performance, in this paper, multi-edge-type (MET) normalized scheme is proposed to improve the performance of traditional min-sum algorithm (MSA) and its modified versions. With respect to sum-product algorithm (SPA), we firstly analyze and find out that the degradations of convergence in different edge types are distinct in MSA theoretically. To compensate the different degradations above, proposed MET-normalized scheme is used in normalized min-sum algorithm (MET-NMSA). In addition, MET-based density evolution (MET-DE) is also presented to search optimized MET-scaling factors for MET-NMSA. To further verify the validity of MET-normalized scheme, Advanced Television Systems Committee (ATSC) 3.0 LDPC codes are used to evaluate MET-NMSA in comparison with the conventional algorithms, i.e., normalized min-sum algorithm (NMSA), offset min-sum algorithm (OMSA) and variable-scaling normalized min-sum algorithm (VS-NMSA). Extensive simulation results show that MET-NMSA for ATSC 3.0 LDPC decoders has at most 1.53dB, 0.21dB and 0.35dB gain over NMSA, OMSA and VS-NMSA respectively when frame error rate (FER) is at 10-4level over additive white Gaussian noise (AWGN) channels using QPSK modulation.
The Sum Product Algorithm (SPA) is known to offer the best performance in decoding large block length Low Density Parity Check (LDPC) codes. However, modifications in SPA to decrease the computation complexity have resulted in performance degradation. The Min Sum Algorithm (MSA) is one such variant, where the computation of the check-to-variable message is simplified to a minimum operation, instead of a hyperbolic tan calculation. Several modifications have been proposed in order to recover the performance loss of the MSA with respect to SPA. This paper proposes a modification to the MSA, based on the Wiener and Linear Minimum Mean Square Error (LMMSE) estimators for LDPC codes. The golden section search algorithm has been used to optimize the computations of the parameter estimation. Simulation results with these estimated parameters show that for low values of SNR, the modified algorithm outperforms MSA and provides performance close to that of SPA with a gain of 0.1 dB. For higher values of SNR, it outperforms MSA with a gain of 1.75 dB while providing an acceptable performance degradation with respect to SPA.