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 journal of advance research, ideas and innovations in technology

A Novel Approach for Efficient LDPC Decoding

B. LasyaSri, B. Ashok Raj, Lavadya Nirmala Devi

Published May 15, 2017• 0 citations
OpenAlex

Abstract

Recently, LDPC codes have been proved to be capable of closely approaching the channel capacity and hence they are strongly promoted in many international standards. Though decoding is simpler compared to Turbo code decoding, efficient decoding techniques for LDPC codes are in demand to make it further simpler. The theoretical performance of LDPC codes appears simple and close to Shannon’s capacity of channel, but the practical implementation is still challenging due to tasks like numerical inaccuracy, limited memory resources, etc. We investigate methods to reduce the complexity and make decoding simple while still keeping the loss in performance negligible. The aim of this paper is to reduce the complexity by simplification of the component decoders. For this, we analyze the min-sum algorithm and derive a theoretical framework. With this framework, we are able to modify the algorithm in order to achieve good performance for regular as well as irregular LDPC codes.

Related papers

Novel LDPC coding and decoding strategies : design, analysis, and algorithms

Jingjing Liu

In this digital era, modern communication systems play an essential part in nearly every aspect of life, with examples ranging from mobile networks and satellite communications to Internet and data transfer. Unfortunately, all communication systems in a practical setting are noisy, which indicates that we can either improve the physical characteristics of the channel or find a possible systematical solution, i.e. error control coding. The history of error control coding dates back to 1948 when Claude Shannon published his celebrated work “A Mathematical Theory of Communication”, which built a framework for channel coding, source coding and information theory. For the first time, we saw evidence for the existence of channel codes, which enable reliable communication as long as the information rate of the code does not surpass the so-called channel capacity. Nevertheless, in the following 60 years none of the codes have been proven closely to approach the theoretical bound until the arrival of turbo codes and the renaissance of LDPC codes. As a strong contender of turbo codes, the advantages of LDPC codes include parallel implementation of decoding algorithms and, more crucially, graphical construction of codes. However, there are also some drawbacks to LDPC codes, e.g. significant performance degradation due to the presence of short cycles or very high decoding latency. In this thesis, we will focus on the practical realisation of finite-length LDPC codes and devise algorithms to tackle those issues. Firstly, rate-compatible (RC) LDPC codes with short/moderate block lengths are investigated on the basis of optimising the graphical structure of the tanner graph (TG), in order to achieve a variety of code rates (0.1 < R < 0.9) by only using a single encoder-decoder pair. As is widely recognised in the literature, the presence of short cycles considerably reduces the overall performance of LDPC codes which significantly limits their application in communication systems. To reduce the impact of short cycles effectively for different code rates, algorithms for counting short cycles and a graph-related metric called Extrinsic Message Degree (EMD) are applied with the development of the proposed puncturing and extension techniques. A complete set of simulations are carried out to demonstrate that the proposed RC designs can largely minimise the performance loss caused by puncturing or extension. Secondly, at the decoding end, we study novel decoding strategies which compensate for the negative effect of short cycles by reweighting part of the extrinsic messages exchanged between the nodes of a TG. The proposed reweighted belief propagation (BP) algorithms aim to implement efficient decoding, i.e. accurate signal reconstruction and low decoding latency, for LDPC codes via various design methods. A variable factor appearance probability belief propagation (VFAP-BP) algorithm is proposed along with an improved version called a locally-optimized reweighted (LOW)-BP algorithm, both of which can be employed to enhance decoding performance significantly for regular and irregular LDPC codes. More importantly, the optimisation of reweighting parameters only takes place in an offline stage so that no additional computational complexity is required during the real-time decoding process. Lastly, two iterative detection and decoding (IDD) receivers are presented for multiple-input multiple-output (MIMO) systems operating in a spatial multiplexing configuration. QR decomposition (QRD)-type IDD receivers utilise the proposed multiple-feedback (MF)-QRD or variable-M (VM)-QRD detection algorithm with a standard BP decoding algorithm, while knowledge-aided (KA)-type receivers are equipped with a simple soft parallel interference cancellation (PIC) detector and the proposed reweighted BP decoders. In the uncoded scenario, the proposed MF-QRD and VM-QRD algorithms are shown to approach optimal performance, yet require a reduced computational complexity. In the LDPC-coded scenario, simulation results have illustrated that the proposed QRD-type IDD receivers can offer near-optimal performance after a small number of detection/decoding iterations and the proposed KA-type IDD receivers significantly outperform receivers using alternative decoding algorithms, while requiring similar decoding complexity.

•Dec 18, 2012•2 citations

Memory-Efficient Sum–Product Decoding of LDPC Codes

H. Sankar, Krishna R. Narayanan

Low-density parity-check (LDPC) codes perform very close to capacity for long lengths on several channels. However, the amount of memory (fixed-point numbers that need to be stored) required for implementing the message-passing algorithm increases linearly as the number of edges in the graph increases. In this letter, we propose a decoding algorithm for decoding LDPC codes that reduces the memory requirement at the decoder. The proposed decoding algorithm can be analyzed using density evolution; further, we show how to design good LDPC codes using this. Results show that this algorithm provides almost the same performance as the conventional sum-product decoding of LDPC codes.

IEEE Transactions on Communications•Aug 1, 2004•28 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

A Low-complexity Iterative Decoding Algorithm for LDPC Codes

Pan Yu

Among the decoding algorithms for low-density parity-check(LDPC) code,sum-product algorithm(SPA) has the optimal performance but high complexity,while min-sum algorithm has simple implementation complexity but worse performance.Considering this performance-complexity contradiction,some modified min-sum algorithms are proposed.In this paper,researches are done based on one of the modified min-sum algorithms that is close to SPA in performance but the way modifying fraction works is simplified.Simplified algorithm remains similar in performance to sum-product algorithm but has a remarkably reduced implementation complexity.

Telecommunication Engineering•Jan 1, 2006•1 citation

Reduced Complexity of Decoding Algorithm for Irregular LDPC Codes Using a Split Row Method

Rachid El Alami, Mostafa Mrabti, Cheikh Bamba Gueye

In this paper, we have proposed a novel method of decoding algorithm of irregular LDPC codes. A reduced complexity LDPC decoding method for regular LDPC code is extended to irregular LDPC codes. We present in this paper a full description of this method and its benefits for various row weight and length code word. The Split-Row method makes column processing parallelism easier to exploit and significantly simplifies row processors. Recently, irregular LDPC codes have received a lot of attention by many advanced standard, such as WiFi, WiMAX Mobile and digital video broadcasting (DVB-S2). Hence the idea to develop the “Split-Row Method” for irregular LDPC codes. In this context, we have performed an implementation on MATLAB of an irregular LDPC codes with different code word and code rate; simulation results over an additive white Gaussian channel show that the error performance of high row-weight codes with Split-Row decoding is within 0.3–0.5 dB of the Min-Sum algorithm. The study result shows that the “Split Row Method” is better for irregular code than regular LDPC codes.

Journal of Wireless Networking and Communications•Aug 31, 2012•5 citations

Min-sum Integer Decoding for LDPC in QPSK Modulation

Peng Xin

Low-Density Parity-Check(LDPC) codes are typical of preeminent performance approaching Shannon’s capacity limit.This paper studies the LDPC codes min-sum decoding algorithm,and a min-sum algorithm in QPSK modulation based on integer operation is proposed for decoding LDPC codes.All the variables are fixed length integers in this algorithm,so it is very convenient for hardware implementation.Simulation results show that its performance is close to that of sum-product algorithm whose variables are high precision floating point numbers.

•Jan 1, 2010•0 citations
Recently, LDPC codes have been proved to be capable of closely approaching the channel capacity and hence they are strongly promoted in many international standards. Though decoding is simpler compared to Turbo code decoding, efficient decoding techniques for LDPC codes are in demand to make it further simpler. The theoretical performance of LDPC codes appears simple and close to Shannon’s capacity of channel, but the practical implementation is still challenging due to tasks like numerical inaccuracy, limited memory resources, etc. We investigate methods to reduce the complexity and make decoding simple while still keeping the loss in performance negligible. The aim of this paper is to reduce the complexity by simplification of the component decoders. For this, we analyze the min-sum algorithm and derive a theoretical framework. With this framework, we are able to modify the algorithm in order to achieve good performance for regular as well as irregular LDPC codes.
In this digital era, modern communication systems play an essential part in nearly every aspect of life, with examples ranging from mobile networks and satellite communications to Internet and data transfer. Unfortunately, all communication systems in a practical setting are noisy, which indicates that we can either improve the physical characteristics of the channel or find a possible systematical solution, i.e. error control coding. The history of error control coding dates back to 1948 when Claude Shannon published his celebrated work “A Mathematical Theory of Communication”, which built a framework for channel coding, source coding and information theory. For the first time, we saw evidence for the existence of channel codes, which enable reliable communication as long as the information rate of the code does not surpass the so-called channel capacity. Nevertheless, in the following 60 years none of the codes have been proven closely to approach the theoretical bound until the arrival of turbo codes and the renaissance of LDPC codes. As a strong contender of turbo codes, the advantages of LDPC codes include parallel implementation of decoding algorithms and, more crucially, graphical construction of codes. However, there are also some drawbacks to LDPC codes, e.g. significant performance degradation due to the presence of short cycles or very high decoding latency. In this thesis, we will focus on the practical realisation of finite-length LDPC codes and devise algorithms to tackle those issues. Firstly, rate-compatible (RC) LDPC codes with short/moderate block lengths are investigated on the basis of optimising the graphical structure of the tanner graph (TG), in order to achieve a variety of code rates (0.1 < R < 0.9) by only using a single encoder-decoder pair. As is widely recognised in the literature, the presence of short cycles considerably reduces the overall performance of LDPC codes which significantly limits their application in communication systems. To reduce the impact of short cycles effectively for different code rates, algorithms for counting short cycles and a graph-related metric called Extrinsic Message Degree (EMD) are applied with the development of the proposed puncturing and extension techniques. A complete set of simulations are carried out to demonstrate that the proposed RC designs can largely minimise the performance loss caused by puncturing or extension. Secondly, at the decoding end, we study novel decoding strategies which compensate for the negative effect of short cycles by reweighting part of the extrinsic messages exchanged between the nodes of a TG. The proposed reweighted belief propagation (BP) algorithms aim to implement efficient decoding, i.e. accurate signal reconstruction and low decoding latency, for LDPC codes via various design methods. A variable factor appearance probability belief propagation (VFAP-BP) algorithm is proposed along with an improved version called a locally-optimized reweighted (LOW)-BP algorithm, both of which can be employed to enhance decoding performance significantly for regular and irregular LDPC codes. More importantly, the optimisation of reweighting parameters only takes place in an offline stage so that no additional computational complexity is required during the real-time decoding process. Lastly, two iterative detection and decoding (IDD) receivers are presented for multiple-input multiple-output (MIMO) systems operating in a spatial multiplexing configuration. QR decomposition (QRD)-type IDD receivers utilise the proposed multiple-feedback (MF)-QRD or variable-M (VM)-QRD detection algorithm with a standard BP decoding algorithm, while knowledge-aided (KA)-type receivers are equipped with a simple soft parallel interference cancellation (PIC) detector and the proposed reweighted BP decoders. In the uncoded scenario, the proposed MF-QRD and VM-QRD algorithms are shown to approach optimal performance, yet require a reduced computational complexity. In the LDPC-coded scenario, simulation results have illustrated that the proposed QRD-type IDD receivers can offer near-optimal performance after a small number of detection/decoding iterations and the proposed KA-type IDD receivers significantly outperform receivers using alternative decoding algorithms, while requiring similar decoding complexity.
Low-density parity-check (LDPC) codes perform very close to capacity for long lengths on several channels. However, the amount of memory (fixed-point numbers that need to be stored) required for implementing the message-passing algorithm increases linearly as the number of edges in the graph increases. In this letter, we propose a decoding algorithm for decoding LDPC codes that reduces the memory requirement at the decoder. The proposed decoding algorithm can be analyzed using density evolution; further, we show how to design good LDPC codes using this. Results show that this algorithm provides almost the same performance as the conventional sum-product decoding of LDPC codes.
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.
Among the decoding algorithms for low-density parity-check(LDPC) code,sum-product algorithm(SPA) has the optimal performance but high complexity,while min-sum algorithm has simple implementation complexity but worse performance.Considering this performance-complexity contradiction,some modified min-sum algorithms are proposed.In this paper,researches are done based on one of the modified min-sum algorithms that is close to SPA in performance but the way modifying fraction works is simplified.Simplified algorithm remains similar in performance to sum-product algorithm but has a remarkably reduced implementation complexity.
In this paper, we have proposed a novel method of decoding algorithm of irregular LDPC codes. A reduced complexity LDPC decoding method for regular LDPC code is extended to irregular LDPC codes. We present in this paper a full description of this method and its benefits for various row weight and length code word. The Split-Row method makes column processing parallelism easier to exploit and significantly simplifies row processors. Recently, irregular LDPC codes have received a lot of attention by many advanced standard, such as WiFi, WiMAX Mobile and digital video broadcasting (DVB-S2). Hence the idea to develop the “Split-Row Method” for irregular LDPC codes. In this context, we have performed an implementation on MATLAB of an irregular LDPC codes with different code word and code rate; simulation results over an additive white Gaussian channel show that the error performance of high row-weight codes with Split-Row decoding is within 0.3–0.5 dB of the Min-Sum algorithm. The study result shows that the “Split Row Method” is better for irregular code than regular LDPC codes.
Low-Density Parity-Check(LDPC) codes are typical of preeminent performance approaching Shannon’s capacity limit.This paper studies the LDPC codes min-sum decoding algorithm,and a min-sum algorithm in QPSK modulation based on integer operation is proposed for decoding LDPC codes.All the variables are fixed length integers in this algorithm,so it is very convenient for hardware implementation.Simulation results show that its performance is close to that of sum-product algorithm whose variables are high precision floating point numbers.