Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on 6G Networking (6GNet)

Quasi-Cyclic Gradient Learning: A Method to Improve Performance of 5G QC-LDPC Codes

Emmanuelle Bodji, Emmanuel Boutillon, Bruno Jahan, Christophe Jégo

Published Dec 17, 2025• 0 citations
Publisher

Abstract

The use of neural networks is advancing across several fields, particularly in digital communications. However, in the domain of error-correcting codes, the prevailing consensus is that Artificial Intelligence (AI) tools can, at best, match the performance of existing methods without offering any significant simplifications or improvements. As a result, the initial enthusiasm for AI-based approaches in this area has substantially declined. Recently, however, it has been demonstrated that gradient descent can be used to guide the optimization process for the code construction of unstructured Low-Density Parity-Check (LDPC) codes. In this paper, we extend and generalize this method to also optimize Quasi-Cyclic LDPC codes (QC-LDPC). More specifically, we propose to apply the new method directly to the base protograph structures of QC-LDPC codes standardized in the fifth generation (5G) New Radio (NR) framework. Experimental results reveal that, for small protograph matrices, the proposed optimization process achieves significant coding gains, with improvements of up to 1.2 dB in signal-to-noise ratio (SNR) at a target frame error rate (FER) of 10−2.

DOI
10.1109/6gnet68413.2025.11314138

Related papers

Optimized Construction of Short and High Rate Protograph QC-LDPC Codes

Jianrong Bao, Xiaorong Xu, Chao Liu +2 more

To obtain efficient and pragmatic channel codes high signal-to-noise ratios (SNRs), an optimized construction of short and high rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is presented. Based on an optimized protograph template, the code framework is firstly produced by the extensions of the variable nodes. By enlarging the dimension of the sub-matrices related to the protograph framework, the base quasi-cyclic (QC) matrix is generated with required code rate and length. Then, the elements in the base matrix are split with even smaller square sub-matrices of the same row and column weights. In this procedure, a progressive edge growth (PEG) algorithm is employed to find the optimized positions of the QC submatrices, which brings larger girth for better code performance. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC improved approximated cycle extrinsic message degree (QCI-ACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph and thus it improves the error floor. Simulation results show that the codes produced by the proposed method demonstrate quite good bit error rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency by the high code rate, as well as the low complexity by the short code length. Therefore, the proposed code construction can be efficiently applied in the design of short and high rate protograph QC-LDPC codes with high rate and rational complexity.

International Conference on Wireless Communications and Signal Processing (WCSP)•Oct 20, 2021•1 citation

Comparative Error Rate Performance Analysis of Quasi Cyclic LDPC Codes For 5G Radio Channel

Sonu Lal, Roopam Gupta, Rakesh Kumar Arya

Fifth Generation New radio (5G) is in final stage for freezing frequency band by Release 16in between 1 GHz to 43 GHz. It is also attracting much attention because of short length and long length data transfer with high speed and low latency time resulting error rate performance will degrade. Researchers are thus in continuous working on construction of more efficient regular Quasi Cyclic LDPC Code with parity check matrices of column weight two on half code rate. We suggest is a construction of regular quasi-cyclic LDPC codes with parity-check matrices of column weight two have good capability to correct bursts errors of erasures that provides benefits in terms of the error rate performance. This paper presents fundamental concepts, review study and comparative analysis which carried out by different methods of constructions QC-LDPC codes for better BER, FER calculation and improved coding gain using latest techniques.

IEEE International Conference on Innovations in High Speed Communication and Signal Processing (IHCSP)•Mar 4, 2023•2 citations

Decoding Optimization for 5G LDPC Codes by Machine Learning

Xiaoning Wu, Ming Jiang, Chunming Zhao

In this paper, we propose a generalized minimum-sum decoding algorithm using a linear approximation (LAMS) for protograph-based low-density parity-check (PB-LDPC) codes with quasi-cyclic (QC) structures. The linear approximation introduces some factors in each decoding iteration, which linearly adjust the check node updating and channel output. These factors are optimized iteratively using machine learning, where the optimization can be efficiently solved by a small and shallow neural network with training data produced by the LAMS decoder. The neural network is built according to the parity check matrix of a PB-LDPC code with a QC structure which can greatly reduce the size of the neural network. Since, we optimize the factors once per decoding iteration, the optimization is not limited by the number of the iterations. Then, we give the optimized results of the factors in the LAMS decoder and perform decoding simulations for PB-LDPC codes in fifth generation mobile networks (5G). In the simulations, the LAMS algorithm shows noticeable improvement over the normalized and the offset minimum-sum algorithms and even better performance than the belief propagation algorithm in some high signal-to-noise ratio regions.

IEEE Access•Jan 1, 2018•69 citations

Absorbing Sets and Error Floor Performance of the 5G New Radio Code

Masoome Otarinia

Low density parity check (LDPC) codes are a class of error correction codes. A structured class of LDPC codes known as quasi cyclic LDPC (QC-LDPC) codes have been selected for the data channels of the new generation of cellular communication standards known as 5G New Radio (NR). LDPC codes are generally decoded using iterative message passing algorithms that yield performance that is close to capacity. Previous research has shown that iterative decoders are vulnerable to certain combinatorial objects in the code’s structure resulting in an error floor, a typically abrupt change of slope in the frame error rate performance curve. These substructures are called absorbing sets; specifically, elementary absorbing sets are found to be particularly impactful for structured LDPC codes. The main focus of this thesis is investigating the decoder performance curve of the 5G NR code and identifying the error prone elementary absorbing sets that contribute to its error floor. In this thesis, we introduce the 5G NR QC-LDPC code and its characteristics; we talk about the measures taken in the transmitter to improve the code’s performance such as puncturing and shortening. We will see how practical limitations such as finite precision (quantization) of LLR values affects the performance in the error floor. We also devise an algorithm to identify all the (elementary) absorbing sets in the code.

•Nov 16, 2022•0 citations

Density Evolution Analysis for 5G NR Quasi-Cyclic Low Density Parity Check (QC-LDPC) Codes

W. Wahidin, Khoirul Anwar, Nachwan Mufti Adriansyah

In this paper, we analyze the performances of the fifth telecommunication generation (5G) new radio (NR) quasi-cyclic (QC) low-density parity check (QC-LDPC) codes via density evolution (DE) for base graph 2 (BG2) over binary erasure channel (BEC). We derive the degree distribution of variable nodes (VND) and check nodes (CND) from the parity check matrix (PCM) of the 3rd Generation Partnership Project (3GPP) TS.38.212 and use them for DE analysis assuming of no cycle or girth. With several number of iterations, we found that 5G NR QC-LDPC of BG2 mother codes have a threshold of $\in$=0.2809. The DE analysis shows that the rateless capability with the extended parity successfully correct the error for higher $\in$, without suffering from the error-floor (although many degree-Is exist), but slightly loose in gap from the Shannon limit. We expect that these results are useful for the future development of QC-LDPC codes for possible improvement in the sixth telecommunication generation (6G).

International Conference on Artificial Intelligence, Blockchain, Cloud Computing, and Data Analytics (ICoABCD)•Nov 13, 2023•3 citations

CODING SCHEME IN NETWORKS USING QUASI CYCLIC LOW DENSITY PARITY CHECK CODES GENERATION WITH SVM

Jayasri Subramaniam, Kousik Nalliyanna Goundar Veerappan

Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes are highly effective error correction codes due to their structured sparsity, providing low complexity and superior error performance. However, improving their performance with modern classification techniques remains a challenge. This study integrates Support Vector Machine (SVM) generation with QC-LDPC codes to optimize error correction efficiency. The proposed approach combines the robust coding properties of QC-LDPC codes with SVM’s decision boundary characteristics, enhancing decoding accuracy. Simulation results show that for a code length of 1024 bits, the Bit Error Rate (BER) improved by 15%, while the Frame Error Rate (FER) reduced by 10% compared to traditional QC-LDPC methods. These improvements underscore the potential of SVMs in refining error correction processes for communication systems, particularly in scenarios with high noise interference.

ICTACT Journal on Data Science and Machine Learning•Sep 1, 2024•0 citations
The use of neural networks is advancing across several fields, particularly in digital communications. However, in the domain of error-correcting codes, the prevailing consensus is that Artificial Intelligence (AI) tools can, at best, match the performance of existing methods without offering any significant simplifications or improvements. As a result, the initial enthusiasm for AI-based approaches in this area has substantially declined. Recently, however, it has been demonstrated that gradient descent can be used to guide the optimization process for the code construction of unstructured Low-Density Parity-Check (LDPC) codes. In this paper, we extend and generalize this method to also optimize Quasi-Cyclic LDPC codes (QC-LDPC). More specifically, we propose to apply the new method directly to the base protograph structures of QC-LDPC codes standardized in the fifth generation (5G) New Radio (NR) framework. Experimental results reveal that, for small protograph matrices, the proposed optimization process achieves significant coding gains, with improvements of up to 1.2 dB in signal-to-noise ratio (SNR) at a target frame error rate (FER) of 10−2.
To obtain efficient and pragmatic channel codes high signal-to-noise ratios (SNRs), an optimized construction of short and high rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is presented. Based on an optimized protograph template, the code framework is firstly produced by the extensions of the variable nodes. By enlarging the dimension of the sub-matrices related to the protograph framework, the base quasi-cyclic (QC) matrix is generated with required code rate and length. Then, the elements in the base matrix are split with even smaller square sub-matrices of the same row and column weights. In this procedure, a progressive edge growth (PEG) algorithm is employed to find the optimized positions of the QC submatrices, which brings larger girth for better code performance. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC improved approximated cycle extrinsic message degree (QCI-ACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph and thus it improves the error floor. Simulation results show that the codes produced by the proposed method demonstrate quite good bit error rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency by the high code rate, as well as the low complexity by the short code length. Therefore, the proposed code construction can be efficiently applied in the design of short and high rate protograph QC-LDPC codes with high rate and rational complexity.
Fifth Generation New radio (5G) is in final stage for freezing frequency band by Release 16in between 1 GHz to 43 GHz. It is also attracting much attention because of short length and long length data transfer with high speed and low latency time resulting error rate performance will degrade. Researchers are thus in continuous working on construction of more efficient regular Quasi Cyclic LDPC Code with parity check matrices of column weight two on half code rate. We suggest is a construction of regular quasi-cyclic LDPC codes with parity-check matrices of column weight two have good capability to correct bursts errors of erasures that provides benefits in terms of the error rate performance. This paper presents fundamental concepts, review study and comparative analysis which carried out by different methods of constructions QC-LDPC codes for better BER, FER calculation and improved coding gain using latest techniques.
In this paper, we propose a generalized minimum-sum decoding algorithm using a linear approximation (LAMS) for protograph-based low-density parity-check (PB-LDPC) codes with quasi-cyclic (QC) structures. The linear approximation introduces some factors in each decoding iteration, which linearly adjust the check node updating and channel output. These factors are optimized iteratively using machine learning, where the optimization can be efficiently solved by a small and shallow neural network with training data produced by the LAMS decoder. The neural network is built according to the parity check matrix of a PB-LDPC code with a QC structure which can greatly reduce the size of the neural network. Since, we optimize the factors once per decoding iteration, the optimization is not limited by the number of the iterations. Then, we give the optimized results of the factors in the LAMS decoder and perform decoding simulations for PB-LDPC codes in fifth generation mobile networks (5G). In the simulations, the LAMS algorithm shows noticeable improvement over the normalized and the offset minimum-sum algorithms and even better performance than the belief propagation algorithm in some high signal-to-noise ratio regions.
Low density parity check (LDPC) codes are a class of error correction codes. A structured class of LDPC codes known as quasi cyclic LDPC (QC-LDPC) codes have been selected for the data channels of the new generation of cellular communication standards known as 5G New Radio (NR). LDPC codes are generally decoded using iterative message passing algorithms that yield performance that is close to capacity. Previous research has shown that iterative decoders are vulnerable to certain combinatorial objects in the code’s structure resulting in an error floor, a typically abrupt change of slope in the frame error rate performance curve. These substructures are called absorbing sets; specifically, elementary absorbing sets are found to be particularly impactful for structured LDPC codes. The main focus of this thesis is investigating the decoder performance curve of the 5G NR code and identifying the error prone elementary absorbing sets that contribute to its error floor. In this thesis, we introduce the 5G NR QC-LDPC code and its characteristics; we talk about the measures taken in the transmitter to improve the code’s performance such as puncturing and shortening. We will see how practical limitations such as finite precision (quantization) of LLR values affects the performance in the error floor. We also devise an algorithm to identify all the (elementary) absorbing sets in the code.
In this paper, we analyze the performances of the fifth telecommunication generation (5G) new radio (NR) quasi-cyclic (QC) low-density parity check (QC-LDPC) codes via density evolution (DE) for base graph 2 (BG2) over binary erasure channel (BEC). We derive the degree distribution of variable nodes (VND) and check nodes (CND) from the parity check matrix (PCM) of the 3rd Generation Partnership Project (3GPP) TS.38.212 and use them for DE analysis assuming of no cycle or girth. With several number of iterations, we found that 5G NR QC-LDPC of BG2 mother codes have a threshold of ∈\in∈=0.2809. The DE analysis shows that the rateless capability with the extended parity successfully correct the error for higher ∈\in∈, without suffering from the error-floor (although many degree-Is exist), but slightly loose in gap from the Shannon limit. We expect that these results are useful for the future development of QC-LDPC codes for possible improvement in the sixth telecommunication generation (6G).
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes are highly effective error correction codes due to their structured sparsity, providing low complexity and superior error performance. However, improving their performance with modern classification techniques remains a challenge. This study integrates Support Vector Machine (SVM) generation with QC-LDPC codes to optimize error correction efficiency. The proposed approach combines the robust coding properties of QC-LDPC codes with SVM’s decision boundary characteristics, enhancing decoding accuracy. Simulation results show that for a code length of 1024 bits, the Bit Error Rate (BER) improved by 15%, while the Frame Error Rate (FER) reduced by 10% compared to traditional QC-LDPC methods. These improvements underscore the potential of SVMs in refining error correction processes for communication systems, particularly in scenarios with high noise interference.