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 Artificial Intelligence, Blockchain, Cloud Computing, and Data Analytics (ICoABCD)

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

W. Wahidin, Khoirul Anwar, Nachwan Mufti Adriansyah

Published Nov 13, 2023• 3 citations
Publisher

Abstract

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).

DOI
10.1109/icoabcd59879.2023.10390907

Related papers

A Design of Layered Decoding for QC-LDPC Codes Based on Reciprocal Channel Approximation

Min Jang, Kyeongyeon Kim, Seho Myung +3 more

This paper presents an analytically designed layered decoding algorithm for quasi-cyclic low-density parity-check (QC-LDPC) codes in the 5th Generation (5G) New Radio (NR) mobile communication system. First, a layered density evolution (DE) based on reciprocal channel approximation (RCA) is newly developed to accurately reflect the layered decoding operation in the decoder design. Using this technique, a single nested sequence is optimized in a greedy way to configure the processing order for any given number of layers. The error-correction performance is improved by up to 0.15 dB, while the number of iterations is reduced by about one simultaneously.

IEEE International Symposium on Information Theory (ISIT)•Jun 26, 2022•6 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

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

Emmanuelle Bodji, Emmanuel Boutillon, Bruno Jahan +1 more

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.

International Conference on 6G Networking (6GNet)•Dec 17, 2025•0 citations

Performance Analysis of Iterative minsum Message Passing Decoding Algorithm for 5G NR LDPC codes

P. Vigneswari, S. Sivakumari

Day by day the internet traffic is increasing rapidly. Challenges to improve these internet traffic requirements leads to evolution of 5G NR LDPC (New Radio Low Density Parity Check) codes which provides high coding gain and energy efficiency. BER Vs Eb/No dB curve defines the energy efficiency and coding gain of the any error correcting codes. LDPC codes which are adopted by 5G Standard are called 5G NR LDPC codes.In the design of the decoder,Message Passing Approach reduces the decoding complexity due to the sparsity of the parity check matrix. An efficient decoding algorithm is the key to the successful code. In this paper an iterative minsum approximation message passing decoding algorithm has been implemented for both BG1 and BG2. Results show that the coding gain can be improved up to 9dB.

International Conference on Intelligent Communication Technologies and Virtual Mobile Networks (ICICV)•Feb 4, 2021•4 citations

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

High-Performance and Low-Complexity Decoding Algorithms for 5G Low-Density Parity-Check Codes

Bich Ngoc Tran-Thi, Truong Nguyen, Trang Hoang

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.

Journal of Communications•Jan 1, 2022•3 citations
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).
This paper presents an analytically designed layered decoding algorithm for quasi-cyclic low-density parity-check (QC-LDPC) codes in the 5th Generation (5G) New Radio (NR) mobile communication system. First, a layered density evolution (DE) based on reciprocal channel approximation (RCA) is newly developed to accurately reflect the layered decoding operation in the decoder design. Using this technique, a single nested sequence is optimized in a greedy way to configure the processing order for any given number of layers. The error-correction performance is improved by up to 0.15 dB, while the number of iterations is reduced by about one simultaneously.
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.
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.
Day by day the internet traffic is increasing rapidly. Challenges to improve these internet traffic requirements leads to evolution of 5G NR LDPC (New Radio Low Density Parity Check) codes which provides high coding gain and energy efficiency. BER Vs Eb/No dB curve defines the energy efficiency and coding gain of the any error correcting codes. LDPC codes which are adopted by 5G Standard are called 5G NR LDPC codes.In the design of the decoder,Message Passing Approach reduces the decoding complexity due to the sparsity of the parity check matrix. An efficient decoding algorithm is the key to the successful code. In this paper an iterative minsum approximation message passing decoding algorithm has been implemented for both BG1 and BG2. Results show that the coding gain can be improved up to 9dB.
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.
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.