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International Conference on Information and Communication Technology Convergence (ICTC)

LNOMS-SS: A Low-Complexity LDPC Decoding Algorithm with Hardware Implementation

Kaishi Wang, Cheng Wang, Songsong Cai, Jiewen Jiang, Xi Gong, Weidong WANG

Published Oct 14, 2025• 0 citations
Publisher

Abstract

With the development of low orbit satellite communication technology, how to improve the communication speed of satellite communication systems and reduce the complexity of system design has become an important research issue. Since the invention of LDPC codes, their excellent decoding performance has been favored by researchers. QC-LDPC codes have become the channel coding scheme for the fifth generation new radio (5G NR) data channel, but at the same time, it has also brought challenges to hardware design. We propose the Layered Normalized Offset Minsum and three layer static scheduling (LNOMS-SS) algorithm. On the basis of the traditional Layered Normalized Minsum algorithm (LNMS) and Layered Offset Minsum algorithm (LOMS), the update order of each layer during hierarchical decoding is determined based on the row weight, column weight, and the number of perforated non-zero elements in the BG matrix. We also implemented the algorithm in hardware and designed an 8-levels LDPC decoder. We proposed innovative designs such as a pre-processing based routing network, a segment approximation based Minsum calculation module, and an improved checksum module. The simulation and implementation results show that our proposed LNOMS-SS algorithm has stronger performance than other algorithms, with lower hardware resource consumption and decoding latency.

DOI
10.1109/ictc66702.2025.11388067

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With the development of low orbit satellite communication technology, how to improve the communication speed of satellite communication systems and reduce the complexity of system design has become an important research issue. Since the invention of LDPC codes, their excellent decoding performance has been favored by researchers. QC-LDPC codes have become the channel coding scheme for the fifth generation new radio (5G NR) data channel, but at the same time, it has also brought challenges to hardware design. We propose the Layered Normalized Offset Minsum and three layer static scheduling (LNOMS-SS) algorithm. On the basis of the traditional Layered Normalized Minsum algorithm (LNMS) and Layered Offset Minsum algorithm (LOMS), the update order of each layer during hierarchical decoding is determined based on the row weight, column weight, and the number of perforated non-zero elements in the BG matrix. We also implemented the algorithm in hardware and designed an 8-levels LDPC decoder. We proposed innovative designs such as a pre-processing based routing network, a segment approximation based Minsum calculation module, and an improved checksum module. The simulation and implementation results show that our proposed LNOMS-SS algorithm has stronger performance than other algorithms, with lower hardware resource consumption and decoding latency.
Entering the 5G era, the hardware design of low-density parity-check (LDPC) codes under the new standard has increasingly higher requirements on throughput. According to the geometric characteristics of the check matrices of the quasi-cyclicQC) LDCP codes under the CCSDS standard, this paper designs a layered dynamic normalized minimum sum algorithm(LDNMSA) under the pre-termination decoding based on de-layering scheme. The check matrix structure of this code is easy for hardware design and the storage resource consumption is low. The approximate replacement of the minimum sum algorithm(MSA) reduces the computational complexity of the check node update process. The determination of correction factors and inter-layer deletion thresholds through computer simulation improves the decoding performance and the speed of a single iteration, and adopt the layered scheduling scheme with optimized update order reduces the number of iterations required for decoding. Experimental results show that when the bit error rate(BER) is 10-5, the designed algorithm has a gain of approximately 0.5 dB compared to the MSA. The speed and calculation amounts to a single iteration are much lower than the log-likelihood-ratio(LLR) belief propagation(BP) algorithm and the performance is only less than 0.1dB.
Quasi-cyclic low-density parity-check (QC-LDPC) codes have been selected as the channel coding scheme for 5G new radio (NR) data channel. In this letter, a novel base graph based static scheduling (BGSS) method is proposed for layered decoding of 5G LDPC codes to accelerate decoding convergence and reduce the average number of iterations (ANI). In the proposed BGSS method, the update order of layers is determined based on row weight, column weight and number of punctured non-zero elements of BG matrix. Three optimization rules are included in BGSS to determine the order: 1) The layer with less punctured non-zero element is updated firstly. 2) The layer with relatively small row weight is updated firstly. 3) The layer which can utilize more recent information is updated firstly. The first rule has the highest priority and the third rule has the lowest priority. Simulation results show that compared with other scheduling method, the proposed method reduces about 1.1 ANI and obtains about 0.05dB performance gain for given LDPC codes.
Abstract In order to cater to the needs of the 5G standard, one of the prominent solutions in terms of high coding gain, high throughput and low power dissipation is the 5G NR LDPC (New Radio Low Density Parity Check) codes which have been adopted by 5G Standard. LDPC codes are the successful Third Generation Forward Error Correcting codes. An Efficient decoder is the key to the success of any Error Correcting Code. LDPC codes are one whose parity check matrix have a very few non zero entries. 5G NR LDPC codes are constructed by Protographs or base graphs and are block structured. This paper improves the performance of Layered Iterative minsum Approximation Message Passing decoding Algorithm using Rate Matching, Fixed Point Quantization and Offset minsum techniques. Rate Matching is to maintain the exact number of encoded blocks with in the TTI. Simulation of this algorithm with BPSK encoding over AWGN channel shows that BER of 10-3 gives Eb/No of~2 dB for the block length of 105.
In this letter, we propose various low-complexity neural layered min-sum (NLMS) algorithms to improve the decoding performance of the fifth generation (5G) new radio (NR) low-density parity-check (LDPC) codes. Our proposals are based on the computationally-efficient normalized offset min-sum (NOMS) approach for the layered belief propagation (LBP). The main novelty of our proposals is a deep neural network (DNN) that implements the layered mode decoding and that additionally learns the normalization and the offset parameters of the NOMS scheme. The schemes that we propose use the DNN as well as adaptation and filtering for estimating the optimum values of these parameters. We show by simulation that our proposed decoders achieve a significant computational benefit compared to the standard (non-neural) LBP decoder without an appreciable performance penalty.
The paper presents a detailed analysis of the minsum decoding algorithm as applied to low-density parity-check (LDPC) codes used in 5G new radio (NR) systems. With the increasing demand for higher data rates and improved reliability in next-generation wireless communications, LDPC codes have emerged as a pivotal component in 5G NR's coding strategy. The minsum algorithm, known for its simplicity and efficiency in message passing, is evaluated in the context of its performance and practical implementation for these codes. Minsum decoding reduces complexity by approximating the soft-decision values using the minimum of the incoming messages, rather than applying the more computationally expensive operations such as hyperbolic tangent functions. In the context of 5G NR, this approximation makes minsum decoding particularly attractive for hardware implementation, providing a good trade-off between error-correction performance and computational efficiency. The algorithm iteratively updates messages passed along the edges of the Tanner graph, leveraging the sparsity of LDPC codes. This abstract reviews the relevance of minsum decoding to 5G NR LDPC codes, emphasizing its role in balancing performance with low computational requirements, critical in mobile and high-throughput applications.
This paper presents a novel approach for the reduced-complexity Min-Sum (MS) decoding of low density parity check (LDPC) codes in the partially parallel layered decoder architecture, which contains large number of serial check node processors. Reduced complexity is obtained by using the variant of the single-minimum Offset Min-Sum (smOMS) algorithm that approximates a second minimum with the addition of the variable weight parameter to the minimum value. Although the reduced-complexity MS algorithms primarily reduce hardware resources in fully parallel implementations, the results showed that a considerable reduction can be obtained if serial check node processors are used. Additionally, the paper proposes a better subminimum estimation for irregular codes from 5G new radio (5G NR). The method uses smaller subminimum estimation weights in check nodes with higher degree and higher weights in check nodes with smaller degree, which lead to the significant improvement in the SNR performance.