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

Communications technology

A Decoding Algorithm Based on ex-LLR Oscillation for Low-Density Parity Check Codes

Yongqiang Gao

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

A great deal of experiment indicate that, during the decoding course of message passing for LDPC codes, a phenomenon of oscillating always exists in some variable messages named extrinsic log-likelihood rate (ex-LLR). It could arose bit error. This paper tells of why the magnitudes of a posterior LLRs and ex-LLRs of some bits would oscillated, and thus two improved algorithms are proposed, which could improve the decoding performance being deteriorated by ex-LLR oscillation. The computer simulation shows that, for short and middle length LDPC codes, the proposed algorithms could lower the error floor without increasing the complexity, so these two algorithms could achieve better BER and BLER than the conventional LLR-BP decoding algorithm.

Related papers

Decoding Algorithms Based on Oscillation for Low-Density Parity Check Codes

Satoshi Gounai

In this paper we focus on the decoding error of the Log-Likelihood Ratio Belief Propagation (LLR-BP) decoding algorithm caused by oscillation. The decoding error caused by the oscillation is dominant in high b/N0 region. Oscillation of the LLR of the extrinsic value in the bit node process (ex-LLR) is propagated to the other bits and affects the whole decoding. The Ordered Statistic Decoding (OSD) algorithm is known to improve the error rate performance of the LLR-BP decoding algorithm. The OSD algorithm is performed by deciding the reliability of each bit based on a posteriori probability. In this paper we propose two decoding algorithms based on two types of oscillations of LLR for LDPC codes. One is the oscillation-based OSD algorithm with deciding the reliability of each bit based on oscillation. The other is the oscillation-based LLR-BP decoding algorithm that modifies ex-LLR based on oscillation. In the oscillation-based LLR-BP decoding algorithm, when ex-LLR oscillates, then we reduce the magnitude of this ex-LLR to reduce the effects on the other bits. Both algorithms improve the decoding errors caused by oscillation. From the computer simulations, we show that paying attention to the oscillation, we can improve the error rate performance of the LLR-BP decoding algorithm.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Aug 1, 2005•22 citations

Modified Belief Propagation Decoding Algorithm for Low-Density Parity Check Code Based on Oscillation

Satoshi Gounai, Tomoaki Otsuki Ohtsuki, T. Kaneko

A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm

IEEE Vehicular Technology Conference•Sep 8, 2006•15 citations

Improved Decoding Algorithms Based on Oscillation Log-likelihood Ratio for Low-density Parity Check Codes

DONG Zijian -, BI Xuyin -

Several decoding algorithms based on oscillation Log-likelihood ratio (LLR) for Lowdensity parity-check (LDPC) codes are investigated in this paper, based on which, an improved decoding algorithm which uses the accumulated LLR as the final bit decision merit is proposed. This approach improves the decoding performance with only a very small increase in storage and computation. Combined with normalized belief-propagation (BP), two algorithms are given, which are named as accumulate normalized BP (ACC-Nor-BP) and compare-add normalized BP (CA-Nor-BP). The storage requirements and computational complexity of ACC-Nor-BP is lower than that of CA-Nor-BP and CA-BP, but performance is close to the CA-Nor-BP and better than CA-BP; therefore ACC-Nor-BP algorithm is an effectively improved BP algorithm which has a good balance between performance and complexity.

INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service Sciences•Sep 30, 2011•1 citation

Design and Implementation of Low Bit Error Rate of LDPC Decoder

Ashlesha P. Kshirsagar, Sandeep Kakde, Manish Devendra Chawhan +1 more

Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.

International Conference on Communication Systems and Network Technologies•Apr 1, 2015•1 citation

Lowering the Error Floor of LDPC Codes by a Two-stage Hybrid Decoding Algorithm

Yueguang Bian, Youzheng Wang, Jing Wang

In this paper, a hybrid decoding scheme is proposed to lower the error floor of low-density parity-check codes. With the observation that some error bits' LLR values oscillate throughout iterative decoding procedure, a "feedback BP" (FBP) decoding algorithm is presented as second-stage decoding cell to reduce the phenomena of oscillations. The hybrid decoding scheme, which consists LLR-BP decoding algorithm and FBP decoding algorithm, detects errors in the codewords obtained by using the parity check equations of LDPC codes. Simulation results show that the new decoding scheme exhibits a lower error floor than that of belief propagation decoding algorithm in the moderate and high SNR region.

International Conference on Communications and Networking in China (ChinaCom)•Aug 1, 2007•0 citations

Hybrid Decoding Algorithm for LDPC Codes with Circles

Li Shuang Hu, Ming Shan Liu, Yuan Zhou +1 more

At present, Low-Density Parity-Check (LDPC) codes widely used in many fields of communications have the best performance of all the Error Correcting Codes (ECC). This paper mainly studies the decoding algorithms of LDPC. It proposes an improved algorithm which is named Check-Variable nodes Hybrid(CVH) algorithm on the basis of the existing algorithms. The CVH algorithm can reduce the computational complexity during the check-node update while overcome with the correlation between the variable-node news in a code with circles. As well as, comparing with the original algorithms the performance of the new one saves 0.1 and 0.3 dB than Log-likelihood Ratios (LLR) Belief Propagation (BP) and BP - based algorithms under Additive White Gaussian Noise (AWGN) channel when the Bit Error Rate (BER) falls to through the simulation. This point shows that this algorithm can increase the decoding performance and reduce the error rate effectively.

Advanced materials research•Jul 1, 2011•0 citations
A great deal of experiment indicate that, during the decoding course of message passing for LDPC codes, a phenomenon of oscillating always exists in some variable messages named extrinsic log-likelihood rate (ex-LLR). It could arose bit error. This paper tells of why the magnitudes of a posterior LLRs and ex-LLRs of some bits would oscillated, and thus two improved algorithms are proposed, which could improve the decoding performance being deteriorated by ex-LLR oscillation. The computer simulation shows that, for short and middle length LDPC codes, the proposed algorithms could lower the error floor without increasing the complexity, so these two algorithms could achieve better BER and BLER than the conventional LLR-BP decoding algorithm.
In this paper we focus on the decoding error of the Log-Likelihood Ratio Belief Propagation (LLR-BP) decoding algorithm caused by oscillation. The decoding error caused by the oscillation is dominant in high b/N0 region. Oscillation of the LLR of the extrinsic value in the bit node process (ex-LLR) is propagated to the other bits and affects the whole decoding. The Ordered Statistic Decoding (OSD) algorithm is known to improve the error rate performance of the LLR-BP decoding algorithm. The OSD algorithm is performed by deciding the reliability of each bit based on a posteriori probability. In this paper we propose two decoding algorithms based on two types of oscillations of LLR for LDPC codes. One is the oscillation-based OSD algorithm with deciding the reliability of each bit based on oscillation. The other is the oscillation-based LLR-BP decoding algorithm that modifies ex-LLR based on oscillation. In the oscillation-based LLR-BP decoding algorithm, when ex-LLR oscillates, then we reduce the magnitude of this ex-LLR to reduce the effects on the other bits. Both algorithms improve the decoding errors caused by oscillation. From the computer simulations, we show that paying attention to the oscillation, we can improve the error rate performance of the LLR-BP decoding algorithm.
A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm
Several decoding algorithms based on oscillation Log-likelihood ratio (LLR) for Lowdensity parity-check (LDPC) codes are investigated in this paper, based on which, an improved decoding algorithm which uses the accumulated LLR as the final bit decision merit is proposed. This approach improves the decoding performance with only a very small increase in storage and computation. Combined with normalized belief-propagation (BP), two algorithms are given, which are named as accumulate normalized BP (ACC-Nor-BP) and compare-add normalized BP (CA-Nor-BP). The storage requirements and computational complexity of ACC-Nor-BP is lower than that of CA-Nor-BP and CA-BP, but performance is close to the CA-Nor-BP and better than CA-BP; therefore ACC-Nor-BP algorithm is an effectively improved BP algorithm which has a good balance between performance and complexity.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
In this paper, a hybrid decoding scheme is proposed to lower the error floor of low-density parity-check codes. With the observation that some error bits' LLR values oscillate throughout iterative decoding procedure, a "feedback BP" (FBP) decoding algorithm is presented as second-stage decoding cell to reduce the phenomena of oscillations. The hybrid decoding scheme, which consists LLR-BP decoding algorithm and FBP decoding algorithm, detects errors in the codewords obtained by using the parity check equations of LDPC codes. Simulation results show that the new decoding scheme exhibits a lower error floor than that of belief propagation decoding algorithm in the moderate and high SNR region.
At present, Low-Density Parity-Check (LDPC) codes widely used in many fields of communications have the best performance of all the Error Correcting Codes (ECC). This paper mainly studies the decoding algorithms of LDPC. It proposes an improved algorithm which is named Check-Variable nodes Hybrid(CVH) algorithm on the basis of the existing algorithms. The CVH algorithm can reduce the computational complexity during the check-node update while overcome with the correlation between the variable-node news in a code with circles. As well as, comparing with the original algorithms the performance of the new one saves 0.1 and 0.3 dB than Log-likelihood Ratios (LLR) Belief Propagation (BP) and BP - based algorithms under Additive White Gaussian Noise (AWGN) channel when the Bit Error Rate (BER) falls to through the simulation. This point shows that this algorithm can increase the decoding performance and reduce the error rate effectively.