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IEEE Transactions on Broadcasting

A Polygonal Line Min-Sum Decoding Scheme for Low Density Parity Check Codes

Yin Xu, Hao Ju, Dazhi He, Na Gao, Yiyan Wu, Yihang Huang, Wenjun Zhang

Published Aug 23, 2021• 7 citations
Publisher

Abstract

Low-density parity-check (LDPC) codes are widely used as error correction codes in new generation digital TV standards, such as the second generation of terrestrial digital video broadcasting standard (DVB-T2), Advanced Television Systems Committee (ATSC) 3.0, etc. The nonlinear belief propagation (BP) algorithm has excellent decoding performance for LDPC codes, but is often simplified in hardware implementations by linear min-sum (MS) algorithm due to its high complexity. This simplification also leads to over-estimation problems, which can be corrected by adding factors in conventional algorithms (e.g., normalized min-sum (NMS), offset min-sum (OMS), and variable scaling normalized min-sum (VMS) algorithms). However, the correction factors of these modified MS algorithms cannot adapt to different channels and modulations, and the performance needs further improvement. In this paper, the concepts of over-estimation value (OEV) and over-estimation rate (OER) are introduced to describe the over-estimation problem of the MS algorithm. Then, under the guidance of OEV and OER, a polygonal line min-sum (PMS) algorithm with correction factors adapted to different channels and modulations is proposed according to LLR distribution. Following the properties of OEV and OER, PMS algorithm is further simplified into Simplified PMS (SPMS) algorithm. LDPC codes from ATSC 3.0 are adopted in this paper to evaluate SPMS algorithm in comparison with the conventional algorithms. Extensive simulation results show that the SPMS algorithm for ATSC 3.0 LDPC decoder has at most 1.61dB, 0.24dB and 0.36dB gain over NMS, OMS and VMS algorithms respectively when frame error rate (FER) is at 10−4level over additive white Gaussian noise (AWGN) channel with QPSK modulation. More importantly, the simulation results show that the SPMS algorithm can achieve much better performance than these modified MS algorithms over AWGN and Rayleigh channel with higher-order modulations or under limited maximum iteration number.

DOI
10.1109/tbc.2021.3105025

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Low-density parity-check (LDPC) codes are widely used as error correction codes in new generation digital TV standards, such as the second generation of terrestrial digital video broadcasting standard (DVB-T2), Advanced Television Systems Committee (ATSC) 3.0, etc. The nonlinear belief propagation (BP) algorithm has excellent decoding performance for LDPC codes, but is often simplified in hardware implementations by linear min-sum (MS) algorithm due to its high complexity. This simplification also leads to over-estimation problems, which can be corrected by adding factors in conventional algorithms (e.g., normalized min-sum (NMS), offset min-sum (OMS), and variable scaling normalized min-sum (VMS) algorithms). However, the correction factors of these modified MS algorithms cannot adapt to different channels and modulations, and the performance needs further improvement. In this paper, the concepts of over-estimation value (OEV) and over-estimation rate (OER) are introduced to describe the over-estimation problem of the MS algorithm. Then, under the guidance of OEV and OER, a polygonal line min-sum (PMS) algorithm with correction factors adapted to different channels and modulations is proposed according to LLR distribution. Following the properties of OEV and OER, PMS algorithm is further simplified into Simplified PMS (SPMS) algorithm. LDPC codes from ATSC 3.0 are adopted in this paper to evaluate SPMS algorithm in comparison with the conventional algorithms. Extensive simulation results show that the SPMS algorithm for ATSC 3.0 LDPC decoder has at most 1.61dB, 0.24dB and 0.36dB gain over NMS, OMS and VMS algorithms respectively when frame error rate (FER) is at 10−4level over additive white Gaussian noise (AWGN) channel with QPSK modulation. More importantly, the simulation results show that the SPMS algorithm can achieve much better performance than these modified MS algorithms over AWGN and Rayleigh channel with higher-order modulations or under limited maximum iteration number.
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.
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 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.
The development of the Fifth Generation (5G) New Radio (NR) provides several significant advantages when compared to the fourth generation (4G) Long Term Evolution (LTE) in mobile communications. Due to the outstanding characteristics of Low-Density Parity-Check (LDPC) codes such as high decoding performance, high throughput, low complexity, they have been accepted as the standard codes for the 5G NR. In this paper, we propose two LDPC decoding algorithms: Hybrid Offset Min-Sum (HOMS) and Variable Offset Min-Sum (VOMS), which are aimed at improving the error correction performance. The main idea of the HOMS/VOMS algorithm is to apply modified factors to both variable-nodes and check-nodes updated processing in order to compensate the extrinsic messages overestimation of the MS-based algorithms and increase the protection ability for degree-1 variable-nodes. The simulation results show that at the Bit-Error-Rate (BER) of 10-5, the proposed HOMS/VOMS algorithm achieves the decoding gain up to 0.2 dB compared to the Offset Min-Sum (OMS) algorithm, with a slight increase in decoding complexity.
This paper proposes a new finite precision iterative decoder for low-density parity-check (LDPC) codes. The proposed decoder, named Sign-Preserving Min-Sum (SP-MS), significantly improves the decoding performance compared to the classical Offset Min-Sum (OMS) decoder when messages are quantized onq=2q=2q=2, 3, or 4 bits. The particularity of the SP-MS decoder is that messages cannot take the 0 value, and can fully benefit from theqqqbits of precision. The optimization of the SP-MS decoder is investigated in the asymptotic limit of the code length using density evolution (DE). Our study shows that 3-bit SP-MS decoders can achieve the same error-correcting performance as 5-bit OMS decoders, and 2-bit SP-MS decoders outperform 3-bit OMS decoders. The finite-length simulations confirm the conclusions of the DE analysis for several LDPC codes. Our SP-MS decoder shows a signal-to-noise ratio (SNR) gain up to 0.43 dB, with a memory/wire reduction of up to 40%, compared to the OMS decoder. Moreover, the SP-MS decoder converges faster and uses fewer iterations than the OMS decoder, with an improvement of up to 83.3% of the average decoding throughput. On an FPGA, the SP-MS decoder reduces resource utilization by up to 56% compared to the OMS decoder.
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 provide optimized offset and scaling values for those LDPC decoders based on Advanced Television Systems Committee (ATSC) 3.0 LDPC codes. Furthermore, according to extensive computer simulations, it is shown that the performance of the OMSA and NMSA with the obtained values is close to that of sum-product algorithm, even though the NMSA-based decoder may show a serious error floor due to a channel mismatch effect. Consequently, we recommend that the ATSC 3.0 transmitters use a concatenation of BCH outer code and LDPC inner code as channel coding, considering the use of NMSA for LDPC decoder in ATSC 3.0 receivers.