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

Journal of Huaihai Institute of Technology

New Encoding/Decoding Scheme for Rotation LDPC Codes

Qiao Guo-lei

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

π-rotation LDPC codes are characterized by their simple encoding structure,little memory requirement and easy circuit implementation.A new regular encoding structure for π-rotation LDPC codes is provided,whose parity check matrix His described by a few indexes and the number of which is less than the code length.This encoding structure is also easy to adjust code rate and code length.A new simple but efficient encoding scheme is also given to encode codeword with the aid of the indexes.Two-dimension arrays are used to store the belief information between check nodes and variable nodes,and then the BP Algorithm is developed.Simulation results indicate that these codes perform as well as regular low-density parity check codes based on completely random matrix constructions.

Related papers

New Min-Sum Decoding Algorithm for π-rotation LDPC Codes

Zijian Dong

π-rotation LDPC codes have many advantages [6] ,such as simple encoding structure,less memory requirement,easy circuit implementation. This paper proposes a new efficient encoding algorithm and a new Min-Sum decoding algorithm for the π-rotation LDPC codes based on the row index matrix and column index matrix of parity check matrix H. Those encoding/decoding algorithms are simple,or even demands no construction of need to construct the real parity check matrix.

Communications technology•Jan 1, 2009•0 citations

The π-rotation low-density parity check codes

Rich Echard, Shih-Chun Chang

We introduce an ensemble of quasi-regular low-density parity check error control codes we call /spl pi/-rotation LDPC codes. These codes are completely defined by a single permutation vector of length n/8 where n is the length of the code. We present an efficient encoding scheme and circuit design based on the single permutation. Simulation results indicate that these codes perform as well as regular low density parity check codes based on completely random matrix constructions. These features make the /spl pi/-rotation code valuable for practical communication system implementation.

Globecom•Nov 13, 2002•51 citations

Parallel reconfigurable decoder architectures for rotation LDPC codes

Zijian Dong, G.-Z. Feng

This study presents a partial-parallel decoder architecture for π-rotation low-density parity-check (LDPC) codes, which have regular rotation structure and linear time encoding architecture. One improved construction method, which deletes one parity-check bit corresponding to the actually redundant weight-1 column, is proposed, and then an effective encoding algorithm, which utilises only the index of one permutation sub-matrix, is presented. Based on the group-structured and permutation characteristics, two-dimensional arrays are used to store the check/variable node information during iterations, and then a cycle reuse mapping architecture is proposed for messages passing among memories, bit functional units (BFUs) and check function units (CFUs). Partial-parallel decoder with this mapping architecture is reconfigurable by only changing four mapping patterns, and needs no address generators which exist in some architecture-aware (AA) LDPC decoders, such as quasi-cyclic LDPC (QC-LDPC) decoders. Simulation results show that the proposed methods are feasible and effective.

IET Communications•Jan 12, 2010•2 citations

Efficient Design of Structured LDPC Codes

Biwoong Chung, Joon-Sung Kim, Song Hong-Yeop

The high encoding complexity of LDPC codes can be solved by designing structured parity-check matrix. If the parity-check matrix of LDPC codes is composed of same type of blocks, decoder implementation can be simple, this structure allow structured decoding and required memory for storing the parity-check matrix can be reduced largely. In this paper, we propose a construction algorithm for short block length structured LDPC codes based on girth condition, PEG algorithm and variable node connectivity. The code designed by this algorithm shows similar performance to other codes without structured constraint in low SNR and better performance in high SNR than those by simulation

한국통신학회논문지•Jan 1, 2006•2 citations

Optimization of Permutation Key for Pi-Rotation LDPC Codes

Nasim Vakili Pourtaklo

The original low-density parity-check (LDPC) codes were developed by Robert Gallager in early 1960 and are based on a random parity-check matrix construction. In the mid 1990's it was discovered that LDPC codes could be modified slightly to provide the more powerful error correction. These newer LDPC codes, based on an irregular column weight in the underlying check matrix, were still defined with random construction techniques. The Pi-rotation LDPC codes discovered by Echard are a family of LDPC codes completely defined by a small set of integers and have several symmetrical features that are exploited to build efficient encoding and decoding designs. The Pi-rotation codes can be extended to include irregular matrix patterns to obtain the highest performance. In this dissertation we develop a heuristic algorithm to find the best parity-check matrix for Pi-rotation LDPC codes.

•May 1, 2006•0 citations

Quasi-cyclic LDPC codes for fast encoding

Seho Myung, Kyeongcheol Yang, Jaeyoel Kim

In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.

IEEE Transactions on Information Theory•Jul 19, 2005•278 citations
π-rotation LDPC codes are characterized by their simple encoding structure,little memory requirement and easy circuit implementation.A new regular encoding structure for π-rotation LDPC codes is provided,whose parity check matrix His described by a few indexes and the number of which is less than the code length.This encoding structure is also easy to adjust code rate and code length.A new simple but efficient encoding scheme is also given to encode codeword with the aid of the indexes.Two-dimension arrays are used to store the belief information between check nodes and variable nodes,and then the BP Algorithm is developed.Simulation results indicate that these codes perform as well as regular low-density parity check codes based on completely random matrix constructions.
We introduce an ensemble of quasi-regular low-density parity check error control codes we call /spl pi/-rotation LDPC codes. These codes are completely defined by a single permutation vector of length n/8 where n is the length of the code. We present an efficient encoding scheme and circuit design based on the single permutation. Simulation results indicate that these codes perform as well as regular low density parity check codes based on completely random matrix constructions. These features make the /spl pi/-rotation code valuable for practical communication system implementation.
This study presents a partial-parallel decoder architecture for π-rotation low-density parity-check (LDPC) codes, which have regular rotation structure and linear time encoding architecture. One improved construction method, which deletes one parity-check bit corresponding to the actually redundant weight-1 column, is proposed, and then an effective encoding algorithm, which utilises only the index of one permutation sub-matrix, is presented. Based on the group-structured and permutation characteristics, two-dimensional arrays are used to store the check/variable node information during iterations, and then a cycle reuse mapping architecture is proposed for messages passing among memories, bit functional units (BFUs) and check function units (CFUs). Partial-parallel decoder with this mapping architecture is reconfigurable by only changing four mapping patterns, and needs no address generators which exist in some architecture-aware (AA) LDPC decoders, such as quasi-cyclic LDPC (QC-LDPC) decoders. Simulation results show that the proposed methods are feasible and effective.
The high encoding complexity of LDPC codes can be solved by designing structured parity-check matrix. If the parity-check matrix of LDPC codes is composed of same type of blocks, decoder implementation can be simple, this structure allow structured decoding and required memory for storing the parity-check matrix can be reduced largely. In this paper, we propose a construction algorithm for short block length structured LDPC codes based on girth condition, PEG algorithm and variable node connectivity. The code designed by this algorithm shows similar performance to other codes without structured constraint in low SNR and better performance in high SNR than those by simulation
The original low-density parity-check (LDPC) codes were developed by Robert Gallager in early 1960 and are based on a random parity-check matrix construction. In the mid 1990's it was discovered that LDPC codes could be modified slightly to provide the more powerful error correction. These newer LDPC codes, based on an irregular column weight in the underlying check matrix, were still defined with random construction techniques. The Pi-rotation LDPC codes discovered by Echard are a family of LDPC codes completely defined by a small set of integers and have several symmetrical features that are exploited to build efficient encoding and decoding designs. The Pi-rotation codes can be extended to include irregular matrix patterns to obtain the highest performance. In this dissertation we develop a heuristic algorithm to find the best parity-check matrix for Pi-rotation LDPC codes.
In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.