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 Computer and Communication Systems (ICCCS)

Decoding of 5G NR Low-Density Parity-Check Codes

Siqi Yu, Francis C. M. Lau, Kunyang Li

Published Apr 19, 2024• 4 citations
Publisher

Abstract

Low-density parity-check (LDPC) codes have been selected as the channel coding scheme for 5G NR standard, which have excellent performance approaching the Shannon limit and are easy to implement in hardware. The decoding algorithm and scheduling scheme of LDPC codes have a significant impact on performance. The row degree (RD) and the number of punctured bits (PBs) are widely used to determine the update order of layers. In this letter, we used Matlab to simulate the error performance of the 5G LDPC codes. We completed the bit error rate and frame error rate simulations of six different decoding algorithms, including flooding LLR-BP, flooding NMS, layered LLR-BP, layered NMS, the lowest degree and least-punctured (LD-LP) layered LLR-BP and LD-LP layered NMS methods, for the 5G LDPC code with a base graph of size [46, 68], code rate 1/3, and code length of 1584.We further compared the performance of LD-LP layered decoding and LP-LD layered decoding. Moreover, we simulated the error performance of the core part of the LDPC code, which consists of four layers. We evaluated the effect of the update order of the four layers on the error performance of the code, and concluded that some update orders might give slightly better error performance than others.

DOI
10.1109/icccs61882.2024.10602849

Related papers

Performance Analysis of Different Flexible Decoding Algorithms for NR-LDPC Codes

Layla Mahdi Salih, Thuraya Mahmood Qaradaghi, Jalal J. Hamad Ameen

Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.

Tikrit Journal of Engineering Sciences•Dec 11, 2022•3 citations

Improving the Performance of Layered Iterative minsum Approximation Message Passing Decoding Algorithm for 5G NR LDPC Codes

P. Vigneswari, S. Sivakumari

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.

Journal of Physics Conference Series•Jun 1, 2021•0 citations

Reordered static layered schedule for 5G low‐density parity‐check codes

Yangcan Zhou, Zhongfeng Wang

Abstract The error performance of the 5G low‐density parity‐check codes is significantly impacted by the update order of layers. At present, the row degree (RD) and the number of punctured bits (PBs) are widely used to decide the update order of layers. Here, the authors propose a metric to assess the soft message recovery speed of coded bits and then suggest updating layers with the lowest RD first rather than those with the least PBs first. Besides, a new criterion is introduced to further determine the update order of layers with the same number of PBs and the same RD. The resulting reordered layered schedule yields better error performance and faster convergence speed than the prior arts.

Electronics Letters•Apr 1, 2024•0 citations

An Analysis and Design of Rate-Dependent Nested Scheduling in Layered Decoding of LDPC Codes

Dongxu Chang, Peng Liu, Guanghui Wang +2 more

In this study, we analyze the characteristics of scheduling sequences for layered belief propagation (LBP) that can result in efficient decoding of low-density parity-check (LDPC) codes. Specifically, we claim that scheduling sequences leading to high decoding efficiency should prioritize updating check nodes with lower error probabilities aggregated from neighboring variable nodes. We prove this conclusion separately on both the BEC and the BI-AWGN channels. Some observable characteristics in “good” scheduling sequences regarding row weights, rows connected to punctured columns, and column weights can serve as corollaries to this conclusion. By comprehensively considering these characteristics of good scheduling, we design a multi-sequence nested scheduling scheme of layered decoding for 5G New Radio (NR) LDPC codes. The proposed schemes can obtain scheduling sequences for various rates of rate-compatible LDPC codes using small hardware storage. What’s more, by respectively storing double-sequence, triple-sequence, or more sequences to obtain scheduling sequences at various code rates, a trade-off can be made between decoder storage and decoding performance. Experimental results demonstrate that the proposed scheme achieves performance improvements compared to existing scheduling schemes at nearly all code rates.

IEEE Transactions on Communications•Jul 3, 2025•2 citations

Performance Simulation of a Layered QC-LDPC Decoder for URLLC Applications

Bilal Mejmaa, Chakir Aqil, Ismail Akharraz +1 more

This research investigates the simulation performance of a layered Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) decoder intended for Ultra-Reliable Low-Latency Communication (URLLC) applications in 5G New-Radio (NR) standards. The proposed work focuses on short block-length QC-LDPC codes (280,176) to meet the dual challenge of achieving ultra-low latency (<1ms) while maintaining high reliability. LDPC codes have traditionally excelled at longer code lengths; this study demonstrates the effectiveness of LDPC codes in short-length contexts through architectural optimization utilizing a layered decoding approach, which provides improved convergence speed and reduced latency compared to traditional flooding techniques. The baseline QC-LDPC decoder performs better in terms of Bit Error Rate (BER) and Block Error Rate (BLER) with only 7 iterations. For a target BLER of 10 −2 , the decoder outperforms reference shorter codes (K40, K64) with an E b /N o gain of up to 0.9 dB.

EPJ Web of Conferences•Jan 1, 2026•0 citations

A Hybrid Decoding Algorithm for Low-Rate LDPC codes in 5G

Kaifei Sun, Ming Jiang

A hybrid decoding algorithm for low-density parity-check codes is presented. The proposed algorithm applies different updating schemes, such as the normalized min-sum (NMS) simplification and linear approximation, to the check-node based on its degree. Meanwhile, to eliminate the dependence on the channel variance estimation, the proposed algorithm adopts a multiplicative factor to initialize the channel input and a fixed linear functions for check-node updating. From the iterative thresholds and decoding simulations, our proposed algorithm can be shown to achieve improved performance (much closer to that of the belief propagation decoding) at the expense of a slight increase in complexity to NMS algorithm.

International Conference on Wireless Communications and Signal Processing (WCSP)•Oct 1, 2018•13 citations
Low-density parity-check (LDPC) codes have been selected as the channel coding scheme for 5G NR standard, which have excellent performance approaching the Shannon limit and are easy to implement in hardware. The decoding algorithm and scheduling scheme of LDPC codes have a significant impact on performance. The row degree (RD) and the number of punctured bits (PBs) are widely used to determine the update order of layers. In this letter, we used Matlab to simulate the error performance of the 5G LDPC codes. We completed the bit error rate and frame error rate simulations of six different decoding algorithms, including flooding LLR-BP, flooding NMS, layered LLR-BP, layered NMS, the lowest degree and least-punctured (LD-LP) layered LLR-BP and LD-LP layered NMS methods, for the 5G LDPC code with a base graph of size [46, 68], code rate 1/3, and code length of 1584.We further compared the performance of LD-LP layered decoding and LP-LD layered decoding. Moreover, we simulated the error performance of the core part of the LDPC code, which consists of four layers. We evaluated the effect of the update order of the four layers on the error performance of the code, and concluded that some update orders might give slightly better error performance than others.
Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.
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.
Abstract The error performance of the 5G low‐density parity‐check codes is significantly impacted by the update order of layers. At present, the row degree (RD) and the number of punctured bits (PBs) are widely used to decide the update order of layers. Here, the authors propose a metric to assess the soft message recovery speed of coded bits and then suggest updating layers with the lowest RD first rather than those with the least PBs first. Besides, a new criterion is introduced to further determine the update order of layers with the same number of PBs and the same RD. The resulting reordered layered schedule yields better error performance and faster convergence speed than the prior arts.
In this study, we analyze the characteristics of scheduling sequences for layered belief propagation (LBP) that can result in efficient decoding of low-density parity-check (LDPC) codes. Specifically, we claim that scheduling sequences leading to high decoding efficiency should prioritize updating check nodes with lower error probabilities aggregated from neighboring variable nodes. We prove this conclusion separately on both the BEC and the BI-AWGN channels. Some observable characteristics in “good” scheduling sequences regarding row weights, rows connected to punctured columns, and column weights can serve as corollaries to this conclusion. By comprehensively considering these characteristics of good scheduling, we design a multi-sequence nested scheduling scheme of layered decoding for 5G New Radio (NR) LDPC codes. The proposed schemes can obtain scheduling sequences for various rates of rate-compatible LDPC codes using small hardware storage. What’s more, by respectively storing double-sequence, triple-sequence, or more sequences to obtain scheduling sequences at various code rates, a trade-off can be made between decoder storage and decoding performance. Experimental results demonstrate that the proposed scheme achieves performance improvements compared to existing scheduling schemes at nearly all code rates.
This research investigates the simulation performance of a layered Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) decoder intended for Ultra-Reliable Low-Latency Communication (URLLC) applications in 5G New-Radio (NR) standards. The proposed work focuses on short block-length QC-LDPC codes (280,176) to meet the dual challenge of achieving ultra-low latency (<1ms) while maintaining high reliability. LDPC codes have traditionally excelled at longer code lengths; this study demonstrates the effectiveness of LDPC codes in short-length contexts through architectural optimization utilizing a layered decoding approach, which provides improved convergence speed and reduced latency compared to traditional flooding techniques. The baseline QC-LDPC decoder performs better in terms of Bit Error Rate (BER) and Block Error Rate (BLER) with only 7 iterations. For a target BLER of 10 −2 , the decoder outperforms reference shorter codes (K40, K64) with an E b /N o gain of up to 0.9 dB.
A hybrid decoding algorithm for low-density parity-check codes is presented. The proposed algorithm applies different updating schemes, such as the normalized min-sum (NMS) simplification and linear approximation, to the check-node based on its degree. Meanwhile, to eliminate the dependence on the channel variance estimation, the proposed algorithm adopts a multiplicative factor to initialize the channel input and a fixed linear functions for check-node updating. From the iterative thresholds and decoding simulations, our proposed algorithm can be shown to achieve improved performance (much closer to that of the belief propagation decoding) at the expense of a slight increase in complexity to NMS algorithm.