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/CIC International Conference on Communications in China (ICCC)

A non-linear LLR approximation for LDPC decoding over impulsive noise channels

Yi Hou, Rongke Liu, Ling Zhao

Published Oct 1, 2014• 9 citations
Publisher

Abstract

The performance of Low-Density Parity-Check codes over symmetric alpha-stable impulsive noise channels is considered in this paper. Due to the lack of closed-form expressions for the probability density functions of almost all the alpha-stable distributions, an efficient non-linear approximation method for channel log-likelihood ratio is presented to achieve high decoding performance covering the range of characteristic exponent from 1 to 2 and avoid the use of complicated numerical integrations. The simulations for both long and short codes show that the parameter selection of the proposed method is not sensitive to the noise level. Even fixed parameter setting for the proposed non-linear approximation can obtain a satisfying decoding performance.

DOI
10.1109/iccchina.2014.7008248

Related papers

Finite Length Analysis of Low-Density Parity-Check Codes on Impulsive Noise Channels

Zhen Mei, Martin Johnston, Stephane Le Goff +1 more

Low-density parity-check (LDPC) codes with very long block lengths are well known for their powerful error correction, but it is not always desirable to employ long codes in communication systems, where latency is a serious issue, such as voice and video communication between multiple users. Finite length analyses of LDPC codes have already been presented in the literature for the additive white Gaussian noise channel, but in this paper, we consider the finite length analysis of LDPC codes for channels that exhibit impulsive noise. First, an exact uncoded bit error probability (BEP) of an impulsive noise channel, modeled as a symmetric α-stable (SαS) distribution, is derived. Then, to obtain the LDPC-coded performance, density evolution is applied to evaluate the asymptotic performance of LDPC codes on SαS channels and determine the threshold signal-to-noise ratio. Finally, we derive closed-form expressions for the BEP and block error probability of short LDPC codes on these channels, which are shown to match closely with simulated results on channels with different levels of impulsiveness, even for block lengths as low as 1000 b.

IEEE Access•Jan 1, 2016•9 citations

Gradient descent bit-flipping based on penalty factor for decoding LDPC codes over symmetric alpha-stable noise channels

Chenyu Gao, Rongke Liu, Bin Dai

A modified gradient descent bit-flipping (GDBF) algorithm is proposed for decoding low-density parity-check (LDPC) codes over the symmetric alpha-stable (SaS) impulsive noise channel. To simplify the log-likelihood rate (LLR) computational implement, this paper introduces a linear approximation of the LLR for the SaS impulsive noise. Combined with the linear approximation, the new algorithm introduces a penalty factor into the syndrome components of the inversion function. Simulation results show that the GDBF algorithm based on the penalty factor performs better than GDBF algorithm.

IEEE/CIC International Conference on Communications in China (ICCC)•Oct 1, 2017•2 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

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

Non-uniform quantization scheme for the decoding of low-density parity-check codes with the sum-product algorithm

Xinru Qu, Liuguo Yin

In this paper, a non-uniform quantization scheme is proposed for the decoding of Low-Density Parity-Check (LDPC) codes with the Sum-Product Algorithm (SPA). With the proposed scheme, the quantization-range and quantization-interval for the soft Log-Likelihood-Ratio (LLR) values of the decoder input, the variable nodes, and the check nodes are set separately, and are also adjusted according to the evolution of the probability density distribution of the LLR values in the iterative decoding procedure to minimize the difference between the decoding values before quantization and that after quantization. Simulation results show that decoding with 3-bit non-uniform quantization of the proposed scheme may obtain a BER performance slightly better than that of decoding with 6-bits quantization of the traditional uniform quantization method.

IEEE International Conference on Electronics Information and Emergency Communication•Jun 1, 2016•5 citations

Efficient early stopping method for LDPC decoding based on check-node messages

Zhaohui Cai, Jianzhong Hao, Ubolthip Sethakaset

An efficient early stopping method is proposed in this paper to reduce the average number of iterations for low density parity check (LDPC) decoders. The method is very efficient especially when the channel signal-to-noise ratio (SNR) is low. It is based on the estimation of the log-likelihood ratio (LLR) messages of the check nodes.

Asilomar Conference on Signals, Systems and Computers (ACSSC)•Oct 1, 2008•2 citations
The performance of Low-Density Parity-Check codes over symmetric alpha-stable impulsive noise channels is considered in this paper. Due to the lack of closed-form expressions for the probability density functions of almost all the alpha-stable distributions, an efficient non-linear approximation method for channel log-likelihood ratio is presented to achieve high decoding performance covering the range of characteristic exponent from 1 to 2 and avoid the use of complicated numerical integrations. The simulations for both long and short codes show that the parameter selection of the proposed method is not sensitive to the noise level. Even fixed parameter setting for the proposed non-linear approximation can obtain a satisfying decoding performance.
Low-density parity-check (LDPC) codes with very long block lengths are well known for their powerful error correction, but it is not always desirable to employ long codes in communication systems, where latency is a serious issue, such as voice and video communication between multiple users. Finite length analyses of LDPC codes have already been presented in the literature for the additive white Gaussian noise channel, but in this paper, we consider the finite length analysis of LDPC codes for channels that exhibit impulsive noise. First, an exact uncoded bit error probability (BEP) of an impulsive noise channel, modeled as a symmetric α-stable (SαS) distribution, is derived. Then, to obtain the LDPC-coded performance, density evolution is applied to evaluate the asymptotic performance of LDPC codes on SαS channels and determine the threshold signal-to-noise ratio. Finally, we derive closed-form expressions for the BEP and block error probability of short LDPC codes on these channels, which are shown to match closely with simulated results on channels with different levels of impulsiveness, even for block lengths as low as 1000 b.
A modified gradient descent bit-flipping (GDBF) algorithm is proposed for decoding low-density parity-check (LDPC) codes over the symmetric alpha-stable (SaS) impulsive noise channel. To simplify the log-likelihood rate (LLR) computational implement, this paper introduces a linear approximation of the LLR for the SaS impulsive noise. Combined with the linear approximation, the new algorithm introduces a penalty factor into the syndrome components of the inversion function. Simulation results show that the GDBF algorithm based on the penalty factor performs better than GDBF algorithm.
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.
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.
In this paper, a non-uniform quantization scheme is proposed for the decoding of Low-Density Parity-Check (LDPC) codes with the Sum-Product Algorithm (SPA). With the proposed scheme, the quantization-range and quantization-interval for the soft Log-Likelihood-Ratio (LLR) values of the decoder input, the variable nodes, and the check nodes are set separately, and are also adjusted according to the evolution of the probability density distribution of the LLR values in the iterative decoding procedure to minimize the difference between the decoding values before quantization and that after quantization. Simulation results show that decoding with 3-bit non-uniform quantization of the proposed scheme may obtain a BER performance slightly better than that of decoding with 6-bits quantization of the traditional uniform quantization method.