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 Electronic Information and Communication Technology (ICEICT)

A construction method of terminated LDPC convolutional codes

Lin Qi, Hao Kang, Tong Liu, Zheng Dou

Published Aug 1, 2016• 0 citations
Publisher

Abstract

LDPC convolutional research has far-reaching significance. Its parity check matrix is periodic, which greatly reduces the encoding process and is easy to implement. And different convolutional LDPC codes can carry on the unified coding to the information blocks of the length transformation. The information transfer efficiency can be improved obviously. In the paper, based on the key problem about the construction of the protograph LDPC convolutional codes, the paper studies boundary extension method and matrix extension algorithm. A series of termination convolutional codes are constructed and the performance simulation is carried out. The experimental results show that the structure of terminated LDPC convolutional codes has a better performance than the protograph LDPC codes in the bit error rate.

DOI
10.1109/iceict.2016.7879667

Related papers

Approaching capacity with asymptotically regular LDPC codes

Michael Lentmaier, Gerhard Paul Fettweis, Kamil Sh. Zigangirov +1 more

We present a family of protograph based LDPC codes that can be derived from permutation matrix based regular (J,K) LDPC convolutional codes by termination. In the terminated protograph, all variable nodes still have degree J but some check nodes at the start and end of the protograph have degrees smaller than K. Since the fraction of these stronger nodes vanishes as the termination length L increases, we call the codes asymptotically regular. The density evolution thresholds of these protographs are better than those of regular (J, K) block codes. Interestingly, this threshold improvement gets stronger with increasing node degrees (at a fixed rate) and it does not decay as L increases. Terminated convolutional protographs can also be derived from standard irregular protographs and may exhibit a significant threshold improvement.

Information Theory and Applications Workshop (ITA)•Feb 1, 2009•94 citations

Design and Analysis of LDPC Convolutional Codes

Arvind Sridharan

Low-density parity-check (LDPC) block codes invented by Gallager in 1962 achieve exceptional error performance on a wide variety of communication channels. LDPC convolutional codes are the convolutional counterparts of LDPC block codes. This dissertation describes techniques for the design of LDPC convolutional codes, and analyzes their distance properties and iterative decoding convergence thresholds. The construction of time invariant LDPC convolutional codes by unwrapping the Tanner graph of algebraically constructed quasi-cyclic LDPC codes is described. The convolutional codes outperform the quasi-cyclic codes from which they are derived. The design of parity-check matrices for time invariant LDPC convolutional codes by the polynomial extension of a base matrix is proposed. An upper bound on free distance, proving that time invariant LDPC codes are not asymptotically good, is obtained. The Tanner graph is used to describe a pipelined message passing based iterative decoder for LDPC convolutional codes that outputs decoding results continuously. The performance of LDPC block and convolutional codes are compared for fixed decoding parameters like computational complexity, processor complexity, and decoding delay. In each case, the LDPC convolutional code performance is at least as good as that of LDPC block codes. An analog circuit to implement pipelined decoding of LDPC convolutional codes is proposed. The distance properties of a permutation matrix based (time varying) ensemble of (J,K) regular LDPC convolutional codes is investigated. It is proved that these codes (for J > 2) have free distance increasing linearly with constraint length, i.e., they are asymptotically good. Further, the asymptotic free distance to constraint length ratio for the convolutional codes is several times larger than the minimum distance to block length ratio for corresponding LDPC block codes. Iterative decoding of terminated LDPC convolutional codes, based on the ensemble mentioned above, is analyzed, assuming transmission over a binary erasure channel. The structured irregularity of the codes leads to significantly better convergence thresholds compared to corresponding LDPC block codes. At the calculated thresholds, both the bit and block error probability can be made arbitrarily small. The results obtained suggest that the thresholds approach capacity with increasing J.

•Sep 15, 2022•30 citations

A Comparison of ARA- and Protograph-Based LDPC Block and Convolutional Codes

Daniel J. Costello, Alí Emre Pusane, Christopher R. Jones +1 more

ARA- and protograph-based LDPC codes are capable of achieving error performance similar to randomly constructed codes while enjoying several implementation advantages as a result of their structure. LDPC convolutional codes can be derived from these codes through an unwrapping process. In this paper, we review the unwrapping process as well as the pipeline decoder that allows continuous decoding of LDPC convolutional codes. Computer simulations are then used to demonstrate that the unwrapped convolutional codes achieve a "convolutional gain" in error performance. We conjecture that this is due to the concatenation of many constraint lengths worth of received symbols in the pipeline decoding process. The consequences of this improved performance are examined in terms of factors related to decoder implementation: processor size, memory requirements, and decoding delay (latency). Finally, given identical protograph kernels, we compare derived block and convolutional codes based on the above measures.

Information Theory and Applications Workshop (ITA)•Jan 1, 2007•17 citations

Construction of protographs for large-girth structured LDPC convolutional codes

Junho Cho, Laurent Schmalen

In this paper, we present a method to construct girth-6 protographs that lead to the shortest constraint length in the convolutional structure. A stringent structural constraint is imposed on the protographs such that the decoder can be implemented efficiently. Then, given the structural constraint, it is shown that finding the aforementioned protographs is equivalent to solving a simple algebraic problem. Based on this mathematical formulation, girth-6 protographs are created without having to resort to a graph search. Using the girth-6 protographs, we derive good low-density parity-check (LDPC) convolutional codes by using periodic quasi-cyclic lifting. The performance of such constructed codes is compared with AR4JA-based LDPC convolutional codes.

International Conference on Communications•Jun 1, 2015•31 citations

Efficient Construction for QC-LDPC Convolutional Codes with Periodic Bit-Filling

Ming Zhao, Zhipeng Liu, Ling Zhao

QC-LDPC-C (Quasi-Cyclic Low Density Parity-Check Convolutional) codes are with low encoding and decoding complexity and can achieve decoding performance approaching the Shannon limit. However, the construction of the parity check matrices need to be free of the length-4 cycles, and the computational complexity of direct construction will increase exponentially without considering the characteristics of the matrices. The construction for QC-LDPC-C codes with periodic bit-filling method is proposed. With the periodicity of the base check matrix, the proposed method firstly fills the deterministic submatrices to realize fast encoding; then it avoids all possible length-4 cycles by periodic filling in the construction of random submatrices. Thus the base check matrix without cycles of length-4 can be obtained, and the girth of expanded check matrix is at least 6. LDPC-C codes with different parameters are used to compare with the constructed QC-LDPC codes. Experimental results show that the codes constructed with proposed method can achieve better performance and lower encoding and decoding complexity.

IEEE International Conference on Computer and Communication Engineering Technology (CCET)•Aug 1, 2018•1 citation

Ensemble of high performance structured binary convolutional LDPC codes with moderate rates

Liwei Mu

An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check (LDPC) codes. Assisted by a proposed partial search algorithm, the polynomialform parity-check matrix of the time-invariant convolutional LDPC code is derived by combining some special codewords of an (n, 2, n - 1) code. The achieved convolutional LDPC codes possess the characteristics of comparatively large girth and given syndrome former memory. The objective of our design is to enable the time-invariant convolutional LDPC codes the advantages of excellent error performance and fast encoding. In particular, the error performance of the proposed convolutional LDPC code with small constraint length is superior to most existing convolutional LDPC codes.

China Communications•Oct 1, 2020•2 citations
LDPC convolutional research has far-reaching significance. Its parity check matrix is periodic, which greatly reduces the encoding process and is easy to implement. And different convolutional LDPC codes can carry on the unified coding to the information blocks of the length transformation. The information transfer efficiency can be improved obviously. In the paper, based on the key problem about the construction of the protograph LDPC convolutional codes, the paper studies boundary extension method and matrix extension algorithm. A series of termination convolutional codes are constructed and the performance simulation is carried out. The experimental results show that the structure of terminated LDPC convolutional codes has a better performance than the protograph LDPC codes in the bit error rate.
We present a family of protograph based LDPC codes that can be derived from permutation matrix based regular (J,K) LDPC convolutional codes by termination. In the terminated protograph, all variable nodes still have degree J but some check nodes at the start and end of the protograph have degrees smaller than K. Since the fraction of these stronger nodes vanishes as the termination length L increases, we call the codes asymptotically regular. The density evolution thresholds of these protographs are better than those of regular (J, K) block codes. Interestingly, this threshold improvement gets stronger with increasing node degrees (at a fixed rate) and it does not decay as L increases. Terminated convolutional protographs can also be derived from standard irregular protographs and may exhibit a significant threshold improvement.
Low-density parity-check (LDPC) block codes invented by Gallager in 1962 achieve exceptional error performance on a wide variety of communication channels. LDPC convolutional codes are the convolutional counterparts of LDPC block codes. This dissertation describes techniques for the design of LDPC convolutional codes, and analyzes their distance properties and iterative decoding convergence thresholds. The construction of time invariant LDPC convolutional codes by unwrapping the Tanner graph of algebraically constructed quasi-cyclic LDPC codes is described. The convolutional codes outperform the quasi-cyclic codes from which they are derived. The design of parity-check matrices for time invariant LDPC convolutional codes by the polynomial extension of a base matrix is proposed. An upper bound on free distance, proving that time invariant LDPC codes are not asymptotically good, is obtained. The Tanner graph is used to describe a pipelined message passing based iterative decoder for LDPC convolutional codes that outputs decoding results continuously. The performance of LDPC block and convolutional codes are compared for fixed decoding parameters like computational complexity, processor complexity, and decoding delay. In each case, the LDPC convolutional code performance is at least as good as that of LDPC block codes. An analog circuit to implement pipelined decoding of LDPC convolutional codes is proposed. The distance properties of a permutation matrix based (time varying) ensemble of (J,K) regular LDPC convolutional codes is investigated. It is proved that these codes (for J > 2) have free distance increasing linearly with constraint length, i.e., they are asymptotically good. Further, the asymptotic free distance to constraint length ratio for the convolutional codes is several times larger than the minimum distance to block length ratio for corresponding LDPC block codes. Iterative decoding of terminated LDPC convolutional codes, based on the ensemble mentioned above, is analyzed, assuming transmission over a binary erasure channel. The structured irregularity of the codes leads to significantly better convergence thresholds compared to corresponding LDPC block codes. At the calculated thresholds, both the bit and block error probability can be made arbitrarily small. The results obtained suggest that the thresholds approach capacity with increasing J.
ARA- and protograph-based LDPC codes are capable of achieving error performance similar to randomly constructed codes while enjoying several implementation advantages as a result of their structure. LDPC convolutional codes can be derived from these codes through an unwrapping process. In this paper, we review the unwrapping process as well as the pipeline decoder that allows continuous decoding of LDPC convolutional codes. Computer simulations are then used to demonstrate that the unwrapped convolutional codes achieve a "convolutional gain" in error performance. We conjecture that this is due to the concatenation of many constraint lengths worth of received symbols in the pipeline decoding process. The consequences of this improved performance are examined in terms of factors related to decoder implementation: processor size, memory requirements, and decoding delay (latency). Finally, given identical protograph kernels, we compare derived block and convolutional codes based on the above measures.
In this paper, we present a method to construct girth-6 protographs that lead to the shortest constraint length in the convolutional structure. A stringent structural constraint is imposed on the protographs such that the decoder can be implemented efficiently. Then, given the structural constraint, it is shown that finding the aforementioned protographs is equivalent to solving a simple algebraic problem. Based on this mathematical formulation, girth-6 protographs are created without having to resort to a graph search. Using the girth-6 protographs, we derive good low-density parity-check (LDPC) convolutional codes by using periodic quasi-cyclic lifting. The performance of such constructed codes is compared with AR4JA-based LDPC convolutional codes.
QC-LDPC-C (Quasi-Cyclic Low Density Parity-Check Convolutional) codes are with low encoding and decoding complexity and can achieve decoding performance approaching the Shannon limit. However, the construction of the parity check matrices need to be free of the length-4 cycles, and the computational complexity of direct construction will increase exponentially without considering the characteristics of the matrices. The construction for QC-LDPC-C codes with periodic bit-filling method is proposed. With the periodicity of the base check matrix, the proposed method firstly fills the deterministic submatrices to realize fast encoding; then it avoids all possible length-4 cycles by periodic filling in the construction of random submatrices. Thus the base check matrix without cycles of length-4 can be obtained, and the girth of expanded check matrix is at least 6. LDPC-C codes with different parameters are used to compare with the constructed QC-LDPC codes. Experimental results show that the codes constructed with proposed method can achieve better performance and lower encoding and decoding complexity.
An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check (LDPC) codes. Assisted by a proposed partial search algorithm, the polynomialform parity-check matrix of the time-invariant convolutional LDPC code is derived by combining some special codewords of an (n, 2, n - 1) code. The achieved convolutional LDPC codes possess the characteristics of comparatively large girth and given syndrome former memory. The objective of our design is to enable the time-invariant convolutional LDPC codes the advantages of excellent error performance and fast encoding. In particular, the error performance of the proposed convolutional LDPC code with small constraint length is superior to most existing convolutional LDPC codes.