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 Transactions on Communications

Construction of Time Invariant Spatially Coupled LDPC Codes Free of Small Trapping Sets

Sima Naseri, Amir H. Banihashemi

Published Feb 22, 2021• 16 citations
Publisher

Abstract

In this paper, we propose a design technique for the construction of variable-regular time-invariant spatially-coupled low-density parity-check (SC-LDPC) codes with small constraint length and low error floor. The proposed technique reduces the error floor by imposing simple constraints on the short cycles in the code's Tanner graph, which in turn, result in the elimination of the most dominant trapping sets of the code. In some cases, we also derive lower bounds on the syndrome former memory for satisfying such constraints. The designed codes are superior to the state-of-the-art in terms of error floor performance and/or decoding complexity and latency.

DOI
10.1109/tcomm.2021.3060797

Related papers

Error Floor Analysis of Quasi-Cyclic LDPC and Spatially Coupled-LDPC Codes and Construction of Codes with Low Error Floor

Sima Naseri

Forward error-correcting (FEC) codes play an important role in transmitting data with extremely high reliability through modern communication systems.Many applications such as optical communication channels require a very low error rate when transmitting data.In this thesis, we study the design and analysis of low-density parity-check (LDPC) codes in general and spatially coupled (SC) LDPC codes in particular.At first, we analyze the error floor performance of finite-length protographbased spatially coupled LDPC codes in terms of their design parameters.We conduct a comprehensive analysis to show that the parameter syndrome former memory (m) plays the main role in the average number of cycles and trapping sets in the Tanner graph of finite-length SC-LDPC codes.This, in fact, gives an insight into the error floor performance of protograph-based SC-LDPC codes, and demonstrates the superiority of these codes in the error floor region, compared to their block code counterparts.To complement the theoretical analysis conducted in the first stage of this research, we develop efficient design techniques for the construction of high-performance quasi-cyclic (QC)-LDPC and SC-LDPC codes, as the second part of the research.Our design approach is basically aimed at improving the performance of finite-length (SC) LDPC codes while maintaining the decoder complexity and latency small.The improvement in error floor is achieved by minimizing (elimination of) the most harmful trapping set (TS)s.In this regard, we present two design approaches: i) imposing simple conditions on the small cycles to result in the elimination of specific classes of trapping sets, ii) developing a search-based design technique such that specific trapping sets are targeted for minimization/elimination through the algorithm.Our constructed QC-LDPC and time-invariant SC-LDPC codes are superior to the stateof-the-art both in terms of their error floor performance and their low decoding latency and complexity.Finally, we look into the design of finite-length time-invariant QC SC-LDPC codes iii I would like to take this opportunity to express my sincere gratitude to my supervisor, Prof. Amir H. Banihashemi, for his invaluable guidance, continuous support and excellent mentorship during the course of my PhD studies.His immense knowledge and supervision always steered me to the right direction during this journey.Besides my supervisor, I would like to thank my committee members for their helpful comments and feedback on this thesis, and for their generosity in contributing their time to serve on my dissertation defense.I would like to mention the government of Ontario in acknowledgment of the Ontario Trillium Scholarship which pledged an ample

•Jan 1, 2021•2 citations

Spatially Coupled LDPC Codes With Small Constraint Length and Low Error Floor

Sima Naseri, Amir H. Banihashemi

In this letter, we design time-invariant spatially coupled low-density parity-check (SC-LDPC) codes with small constraint length and low error floor. For this, we modify the codes in the literature that have (close to) minimal constraint length for a given degree distribution and girth, to improve their error floor. This is performed by eliminating (or minimizing the multiplicity of) some of the dominant trapping sets (TSs) of the codes and/or increasing the minimum distance. To reduce the multiplicity of the TSs effectively and efficiently, we devise a technique based on the parent/child relationship between TSs that aims at successively minimizing the multiplicity of TSs depending on their harmfulness.

IEEE Communications Letters•Nov 26, 2019•21 citations

Time-invariant spatially coupled low-density parity-check codes with small constraint length

Marco Baldi, Massimo Battaglioni, Franco Chiaraluce +1 more

We consider a special family of spatially coupled low-density parity-check (SC-LDPC) codes, that is, time-invariant low-density parity-check convolutional (LDPCC) codes, which are known in the literature for a long time. Codes of this kind are usually designed by starting from quasi-cyclic (QC) block codes, and applying suitable unwrapping procedures. We show that, by directly designing the LDPCC code syndrome former matrix without the constraints of the underlying QC block code, it is possible to achieve smaller constraint lengths with respect to the best solutions available in the literature. We also find theoretical lower bounds on the syndrome former constraint length for codes with a specified minimum length of the local cycles in their Tanner graphs. For this purpose, we exploit a new approach based on a numerical representation of the syndrome former matrix, which generalizes over a technique we already used to study a special subclass of the codes here considered.

arXiv:1605.05560•IEEE International Black Sea Conference on Communications and Networking•Jan 1, 2016•4 citations

Construction of Girth-8 QC-LDPC Codes Free of Small Trapping Sets

Sima Naseri, Amir H. Banihashemi

In this letter, we propose a new technique to design quasi-cyclic low-density parity-check (QC-LDPC) codes with girth 8 and variable node degrees 3 and 4. Small trapping sets are avoided in the designed codes by imposing simple constraints on the cycles of length 8 in the code's Tanner graph. We also derive lower bounds on the block length of the codes that can satisfy such constraints. Simulation results are provided to demonstrate the superiority of the designed codes in comparison with similar codes in the literature.

IEEE Communications Letters•Aug 8, 2019•27 citations

Design of Protograph-Based Quasi-Cyclic Spatially Coupled Ldpc Codes

Shuoshuo Wang, Zhanji Wu, Qihao Wu

In this paper, we deal with time-varing quasi-cyclic (QC) spatially-coupled (SC) low-density parity-check (LDPC) codes by lifting the coupled protographs. The construction method of girth-6 protographs for any code rate is proposed. We provide a theoretical lower bound on the syndrome former constraint length under condition of the protographs without 4-cycles in their Tanner graphs. Then we use periodic QC lifting method to search the QC-SC-LDPC matrices with larger girth based on the protographs. The minimum dimension size of QC-SC-LDPC codes is given to count the girth of QC-SC-LDPC codes with a semi- infinite binary-check matrix structure. The performance of such constructed codes with lower complexity and delay is superior to the LDPC block codes.

IEEE Wireless Communications and Networking Conference Workshops (WCNCW)•Apr 1, 2020•2 citations

On the Construction of LDPC Codes Free of Small Trapping Sets by Controlling Cycles

Xiongfei Tao, Yufei Li, Yonghe Liu +1 more

Low-density parity-check (LDPC) codes exhibit excellent error correcting capability. However, small trapping sets in the Tanner graph are harmful to the iterative decoding algorithm. In this letter, we present a method of constructing (3, n) girth-eight quasi-cyclic LDPC codes with low error floor by removing the small trapping sets from the Tanner graph. To address this issue, we analyze the relationship between eight-cycles and small trapping sets of Tanner graphs based on fully connected base graphs without parallel edges. We find that if some eight-cycles are not found in the Tanner graphs, any elementary trapping set in the range of a ≤ 8 and b ≤ 3 is removed naturally. We also derive a lower bound on the permutation size for the construction of such codes. The experimental simulation shows a favorable error rate performance with lower error floor over additive white Gaussian noise channels.

IEEE Communications Letters•Mar 8, 2017•30 citations
In this paper, we propose a design technique for the construction of variable-regular time-invariant spatially-coupled low-density parity-check (SC-LDPC) codes with small constraint length and low error floor. The proposed technique reduces the error floor by imposing simple constraints on the short cycles in the code's Tanner graph, which in turn, result in the elimination of the most dominant trapping sets of the code. In some cases, we also derive lower bounds on the syndrome former memory for satisfying such constraints. The designed codes are superior to the state-of-the-art in terms of error floor performance and/or decoding complexity and latency.
Forward error-correcting (FEC) codes play an important role in transmitting data with extremely high reliability through modern communication systems.Many applications such as optical communication channels require a very low error rate when transmitting data.In this thesis, we study the design and analysis of low-density parity-check (LDPC) codes in general and spatially coupled (SC) LDPC codes in particular.At first, we analyze the error floor performance of finite-length protographbased spatially coupled LDPC codes in terms of their design parameters.We conduct a comprehensive analysis to show that the parameter syndrome former memory (m) plays the main role in the average number of cycles and trapping sets in the Tanner graph of finite-length SC-LDPC codes.This, in fact, gives an insight into the error floor performance of protograph-based SC-LDPC codes, and demonstrates the superiority of these codes in the error floor region, compared to their block code counterparts.To complement the theoretical analysis conducted in the first stage of this research, we develop efficient design techniques for the construction of high-performance quasi-cyclic (QC)-LDPC and SC-LDPC codes, as the second part of the research.Our design approach is basically aimed at improving the performance of finite-length (SC) LDPC codes while maintaining the decoder complexity and latency small.The improvement in error floor is achieved by minimizing (elimination of) the most harmful trapping set (TS)s.In this regard, we present two design approaches: i) imposing simple conditions on the small cycles to result in the elimination of specific classes of trapping sets, ii) developing a search-based design technique such that specific trapping sets are targeted for minimization/elimination through the algorithm.Our constructed QC-LDPC and time-invariant SC-LDPC codes are superior to the stateof-the-art both in terms of their error floor performance and their low decoding latency and complexity.Finally, we look into the design of finite-length time-invariant QC SC-LDPC codes iii I would like to take this opportunity to express my sincere gratitude to my supervisor, Prof. Amir H. Banihashemi, for his invaluable guidance, continuous support and excellent mentorship during the course of my PhD studies.His immense knowledge and supervision always steered me to the right direction during this journey.Besides my supervisor, I would like to thank my committee members for their helpful comments and feedback on this thesis, and for their generosity in contributing their time to serve on my dissertation defense.I would like to mention the government of Ontario in acknowledgment of the Ontario Trillium Scholarship which pledged an ample
In this letter, we design time-invariant spatially coupled low-density parity-check (SC-LDPC) codes with small constraint length and low error floor. For this, we modify the codes in the literature that have (close to) minimal constraint length for a given degree distribution and girth, to improve their error floor. This is performed by eliminating (or minimizing the multiplicity of) some of the dominant trapping sets (TSs) of the codes and/or increasing the minimum distance. To reduce the multiplicity of the TSs effectively and efficiently, we devise a technique based on the parent/child relationship between TSs that aims at successively minimizing the multiplicity of TSs depending on their harmfulness.
We consider a special family of spatially coupled low-density parity-check (SC-LDPC) codes, that is, time-invariant low-density parity-check convolutional (LDPCC) codes, which are known in the literature for a long time. Codes of this kind are usually designed by starting from quasi-cyclic (QC) block codes, and applying suitable unwrapping procedures. We show that, by directly designing the LDPCC code syndrome former matrix without the constraints of the underlying QC block code, it is possible to achieve smaller constraint lengths with respect to the best solutions available in the literature. We also find theoretical lower bounds on the syndrome former constraint length for codes with a specified minimum length of the local cycles in their Tanner graphs. For this purpose, we exploit a new approach based on a numerical representation of the syndrome former matrix, which generalizes over a technique we already used to study a special subclass of the codes here considered.
In this letter, we propose a new technique to design quasi-cyclic low-density parity-check (QC-LDPC) codes with girth 8 and variable node degrees 3 and 4. Small trapping sets are avoided in the designed codes by imposing simple constraints on the cycles of length 8 in the code's Tanner graph. We also derive lower bounds on the block length of the codes that can satisfy such constraints. Simulation results are provided to demonstrate the superiority of the designed codes in comparison with similar codes in the literature.
In this paper, we deal with time-varing quasi-cyclic (QC) spatially-coupled (SC) low-density parity-check (LDPC) codes by lifting the coupled protographs. The construction method of girth-6 protographs for any code rate is proposed. We provide a theoretical lower bound on the syndrome former constraint length under condition of the protographs without 4-cycles in their Tanner graphs. Then we use periodic QC lifting method to search the QC-SC-LDPC matrices with larger girth based on the protographs. The minimum dimension size of QC-SC-LDPC codes is given to count the girth of QC-SC-LDPC codes with a semi- infinite binary-check matrix structure. The performance of such constructed codes with lower complexity and delay is superior to the LDPC block codes.
Low-density parity-check (LDPC) codes exhibit excellent error correcting capability. However, small trapping sets in the Tanner graph are harmful to the iterative decoding algorithm. In this letter, we present a method of constructing (3, n) girth-eight quasi-cyclic LDPC codes with low error floor by removing the small trapping sets from the Tanner graph. To address this issue, we analyze the relationship between eight-cycles and small trapping sets of Tanner graphs based on fully connected base graphs without parallel edges. We find that if some eight-cycles are not found in the Tanner graphs, any elementary trapping set in the range of a ≤ 8 and b ≤ 3 is removed naturally. We also derive a lower bound on the permutation size for the construction of such codes. The experimental simulation shows a favorable error rate performance with lower error floor over additive white Gaussian noise channels.