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

IEEE International Conference on Information, Communication and Networks (ICICN)

Optimization of LDPC Decoding Algorithms Through Approximation of the Box-Plus Operation

Bo Sun, Leijing Yang, Jialong Ren, Ziye Wang, Yuanxiang Chen

Published Aug 8, 2025• 0 citations
Publisher

Abstract

The high complexity of the Belief Propagation (BP) decoding algorithm in LDPC decoding leads to greater resource consumption and increased communication link latency. This has become a critical challenge in designing efficient communication systems. The Box-Plus operation can effectively transform the nonlinear equations in check nodes into an addition operation of the minimum and the logarithmic functions, but the logarithmic function still has high complexity. In this paper, we propose an Approximate Box-Plus (ABP) decoding algorithm, which reduces decoding complexity while maintaining decoding performance. We first deduced that the logarithmic function in addition operations essentially represents the error between the BP decoding algorithm and the Min-Sum (MS). Based on this insight, a low-complexity, high-precision substitute function is designed. This function utilizes the boundary control ability and symmetry of the min and max functions to effectively express the relative size changes, thereby reducing the unreliability in check node message passing. The proposed decoding algorithm based on the above function reduces the complexity by 38.9% compared to the BP algorithm, and the mean square error of the substitute function and logarithmic function is only 0.0018. Simulation results demonstrate that the decoding performance improves by approximately 0.4 dB compared to the classical Normalized Min-Sum (NMS) and Offset Min-Sum (OMS) algorithms, and the complexity is increased by only three and two new operations per operation compared to NMS and OMS, respectively.

DOI
10.1109/icicn67355.2025.11430448

Related papers

An Improved 5G NR LDPC Decoding Algorithm Based On Box-Plus Operation

Liming Lu, Yi Li, Li Fang

Iterative box-plus operation is an equivalent function of BP algorithm used in fifth generation(5G) new radio Low-Density Parity-Check (LDPC) decoders, which has gathered significant interest in the past few years. However, it is very challenging to approximate iterative Box-Plus operation effectively since it contains continuous logarithmic and exponential operation. In this paper, the problem is solved gracefully by proposing a simple yet efficient approximate function. The corresponding optimal parameters are given by density evolution and Monte Carlo simulation, which could greatly reduce the unreliability of check-to-variable messages. The extensive experiments in error-correction performance have show the feasibility of the proposed method, compared to existing NMS and OMS algorithms, which makes it more attractive in practical 5G LDPC decoding applications.

IEEE/CIC International Conference on Communications in China (ICCC)•Aug 11, 2022•2 citations

An optimized min-sum variable node layering for LDPC decoding

Nassib Laouini, Larbi Ben Hadj Slama, Ammar Bouallègue

Layered decoding is well appreciated in Low-Density Parity-Check (LDPC) decoder implementation since it provides efficient and high-throughput implementation of LDPC decoders. Variable-Node Layered Belief Propagation (VL-BP) algorithm and their reduced-complexity derivatives for LDPC codes are presented. The VL-BP algorithm is a modification of Belief Propagation algorithm (BP), where the variable nodes are divided in subgroups called layers and each iteration is broken into multiple sub-iterations. Some simplifications can also be made to lower the complexity of both BP and CL-BP algorithms, and particularly the complexity of the check node update rule. In this paper, we consider Variable Node Layered BP (VL-BP) algorithm and propose an optimized min-sum VL-BP (MS VL-BP) algorithm for decoding LDPC code which has better performance not only from MS VL-BP algorithm but also from BP algorithm. In this decoding method, unlike other layered algorithms, we consider for the first layer a set of variable nodes that has a low value of the intrinsic information. Simulation results show that good performance can be achieved, and which can even be improved by the addition of either a normalization term or an additive offset term.

•Apr 1, 2014•1 citation

Reduced-Complexity Decoding of LDPC Codes

J. Chen, Ajay Dholakia, Evangelos S. Eleftheriou +2 more

Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.

IEEE Transactions on Communications•Aug 1, 2005•952 citations

Reduced-Complexity Decoding of LDPC Codes

Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.

IEEE Transactions on Communications•Jul 1, 2005•27 citations

New group shuffled BP decoding algorithms for LDPC codes

Chi-Yuan Chang, Yu‐Liang Chen, Chang‐Ming Lee +1 more

Implementing a belief propagation (BP) based LDPC decoder requires high degrees of parallelism using many component soft-in soft-output (SISO) decoding units to perform message passing from variable nodes to check nodes or vice versa. An obvious complexity-reduction solution is to serialize the decoding process, i.e., dividing a decoding iteration into several serial sub-iterations in which a sub-iteration performs only part of the complete parallel message-passing operation. The group horizontal shuffled BP (GHSBP) and vertical shuffled BP (GVSBP) algorithms respectively partition the check and variable nodes of the code graph into groups to perform group-by-group message-passing decoding. This paper proposes new techniques to improve three key elements of a GHSBP decoding algorithm, namely, the grouping method, the decoding schedule and the log-likelihood updating formulae. The (check nodes) grouping method and decoding schedule optimize certain design criterion. The new normalized min-sum updating formula with a self-adjustable correction (scaling) factor offers better nonlinear approximation. Numerical performance of new GHSBP algorithms that include part or all three new techniques indicate that the combination of the proposed grouping and decoding schedule yields a faster convergence rate and our modified min-sum algorithm gives performance superior to that of the conventional min-sum and normalized min-sum algorithm and is very close to that of the sum-product algorithm.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2009•4 citations

Improved LDPC decoding algorithms based on min-sum algorithm

Y.V. A. C. Kumara, Chandika Bandara Wavegedara

Low-Density Parity check (LDPC) codes offer high-performance error correction near the Shannon limit which employs large code lengths and some iterations in the decoding process. The conventional decoding algorithm of LDPC is the Log Likelihood Ratio based Belief Propagation (LLR BP) which is also known as the `Sum-Product algorithm' which gives the best decoding performance and requires the most computational complexity and implementations with increased hardware complexity. Another simpler variant of this algorithm is used which is known as `min-sum algorithm' which reduces computational complexity as well as hardware complexity but with reduced accuracy. This paper analyzes the reason min-sum algorithm is more prone to errors when compared to the sum-product algorithm, and puts forward two improved algorithms which improve the performance of the min-sum algorithm with comparable algorithmic complexity.

Moratuwa Engineering Research Conference (MERCon)•Apr 1, 2016•8 citations
The high complexity of the Belief Propagation (BP) decoding algorithm in LDPC decoding leads to greater resource consumption and increased communication link latency. This has become a critical challenge in designing efficient communication systems. The Box-Plus operation can effectively transform the nonlinear equations in check nodes into an addition operation of the minimum and the logarithmic functions, but the logarithmic function still has high complexity. In this paper, we propose an Approximate Box-Plus (ABP) decoding algorithm, which reduces decoding complexity while maintaining decoding performance. We first deduced that the logarithmic function in addition operations essentially represents the error between the BP decoding algorithm and the Min-Sum (MS). Based on this insight, a low-complexity, high-precision substitute function is designed. This function utilizes the boundary control ability and symmetry of the min and max functions to effectively express the relative size changes, thereby reducing the unreliability in check node message passing. The proposed decoding algorithm based on the above function reduces the complexity by 38.9% compared to the BP algorithm, and the mean square error of the substitute function and logarithmic function is only 0.0018. Simulation results demonstrate that the decoding performance improves by approximately 0.4 dB compared to the classical Normalized Min-Sum (NMS) and Offset Min-Sum (OMS) algorithms, and the complexity is increased by only three and two new operations per operation compared to NMS and OMS, respectively.
Iterative box-plus operation is an equivalent function of BP algorithm used in fifth generation(5G) new radio Low-Density Parity-Check (LDPC) decoders, which has gathered significant interest in the past few years. However, it is very challenging to approximate iterative Box-Plus operation effectively since it contains continuous logarithmic and exponential operation. In this paper, the problem is solved gracefully by proposing a simple yet efficient approximate function. The corresponding optimal parameters are given by density evolution and Monte Carlo simulation, which could greatly reduce the unreliability of check-to-variable messages. The extensive experiments in error-correction performance have show the feasibility of the proposed method, compared to existing NMS and OMS algorithms, which makes it more attractive in practical 5G LDPC decoding applications.
Layered decoding is well appreciated in Low-Density Parity-Check (LDPC) decoder implementation since it provides efficient and high-throughput implementation of LDPC decoders. Variable-Node Layered Belief Propagation (VL-BP) algorithm and their reduced-complexity derivatives for LDPC codes are presented. The VL-BP algorithm is a modification of Belief Propagation algorithm (BP), where the variable nodes are divided in subgroups called layers and each iteration is broken into multiple sub-iterations. Some simplifications can also be made to lower the complexity of both BP and CL-BP algorithms, and particularly the complexity of the check node update rule. In this paper, we consider Variable Node Layered BP (VL-BP) algorithm and propose an optimized min-sum VL-BP (MS VL-BP) algorithm for decoding LDPC code which has better performance not only from MS VL-BP algorithm but also from BP algorithm. In this decoding method, unlike other layered algorithms, we consider for the first layer a set of variable nodes that has a low value of the intrinsic information. Simulation results show that good performance can be achieved, and which can even be improved by the addition of either a normalization term or an additive offset term.
Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.
Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.
Implementing a belief propagation (BP) based LDPC decoder requires high degrees of parallelism using many component soft-in soft-output (SISO) decoding units to perform message passing from variable nodes to check nodes or vice versa. An obvious complexity-reduction solution is to serialize the decoding process, i.e., dividing a decoding iteration into several serial sub-iterations in which a sub-iteration performs only part of the complete parallel message-passing operation. The group horizontal shuffled BP (GHSBP) and vertical shuffled BP (GVSBP) algorithms respectively partition the check and variable nodes of the code graph into groups to perform group-by-group message-passing decoding. This paper proposes new techniques to improve three key elements of a GHSBP decoding algorithm, namely, the grouping method, the decoding schedule and the log-likelihood updating formulae. The (check nodes) grouping method and decoding schedule optimize certain design criterion. The new normalized min-sum updating formula with a self-adjustable correction (scaling) factor offers better nonlinear approximation. Numerical performance of new GHSBP algorithms that include part or all three new techniques indicate that the combination of the proposed grouping and decoding schedule yields a faster convergence rate and our modified min-sum algorithm gives performance superior to that of the conventional min-sum and normalized min-sum algorithm and is very close to that of the sum-product algorithm.
Low-Density Parity check (LDPC) codes offer high-performance error correction near the Shannon limit which employs large code lengths and some iterations in the decoding process. The conventional decoding algorithm of LDPC is the Log Likelihood Ratio based Belief Propagation (LLR BP) which is also known as the `Sum-Product algorithm' which gives the best decoding performance and requires the most computational complexity and implementations with increased hardware complexity. Another simpler variant of this algorithm is used which is known as `min-sum algorithm' which reduces computational complexity as well as hardware complexity but with reduced accuracy. This paper analyzes the reason min-sum algorithm is more prone to errors when compared to the sum-product algorithm, and puts forward two improved algorithms which improve the performance of the min-sum algorithm with comparable algorithmic complexity.