Codes on finite geometries

@article{Tang2005CodesOF,
  title={Codes on finite geometries},
  author={Heng Tang and Jun Xu and Shu Lin and Khaled A. S. Abdel-Ghaffar},
  journal={IEEE Transactions on Information Theory},
  year={2005},
  volume={51},
  pages={572-596}
}
New algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented. The new construction methods result in a class of multistep majority-logic decodable codes and three classes of low-density parity-check (LDPC) codes. Decoding methods for the class of majority-logic decodable codes, and a class of codes that perform well with iterative decoding in spite of having many cycles of length 4 in their Tanner graphs, are presented. Most of… 
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187 Citations
Highly Influential Citations
23
Background Citations
65
Methods Citations
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187 Citations

On a Class of High-Girth LDPC Codes Based on Finite Multidimensional Lattices

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A Euclidean Geometry Based Algebraic Construction Technique for Girth-8 Gallager LDPC Codes

A construction technique is proposed for low-density parity-check (LDPC) codes based on finite Euclidean geometries EG(m,2s), and simulation results show that these codes have very good error-correcting performance.

Construction of nonbinary cyclic, quasi-cyclic and regular LDPC codes: a finite geometry approach

Five methods for constructing nonbinary LDPC codes based on finite geometries are presented and it is shown that constructed codes in these classes decoded with iterative decoding based on belief propagation perform very well over the AWGN channel and they achieve significant coding gains over Reed-Solomon codes.

Design of irregular quasi-cyclic LDPC codes based on Euclidean geometries

  • Xueqin JiangM. Lee
  • Computer Science
    2009 Fourth International Workshop on Signal Design and its Applications in Communications
  • 2009
This paper presents an approach to the construction of low-density parity-check (LDPC) codes based on hyperplanes (μ-flats) of different dimensions in Euclidean geometries and shows that these codes perform very well at both of waterfall region and the error floor region with the iterative decoding.

Construction of irregular quasi-cyclic LDPC codes based on Euclidean geometries

The proposed irregular LDPC codes having flexible column/row weights are obtained with a hyperplane decomposing method in Euclidean geometries and can be optimized by technologies like the curve fitting approach in the extrinsic information transfer (EXIT) charts.

Two Algebraic Methods for Constructing Efficiently Encodable Quasi-Cyclic LDPC Codes

Simulation results show that with SPA decoding, the constructed codes perform very well over the AWGN channel compared to some other types of famous codes, such as random Mackay code or extended EG-LDPC code recommended by NASA.

Generalized quasi-cyclic low-density parity-check codes based on finite geometries

It is proved that several promising classes of codes based on finite geometries cannot be classified as quasi- cyclic (QC) codes but should be included in broader generalized quasi-cyclic (GQC), and an algorithm is proposed for the computation of the Gröbner bases from the parity check matrices of GQC codes.

Combinatorial Construction of Low-Density Parity-Check Codes for Short Block Length and High Rate Applications

Although the Tanner graph of the codes constructed contains some cycles of length 4, simulation results show that they perform well under belief propagation (BP) decoding, and hence can be encoded efficiently.

Large Girth Non-Binary LDPC Codes Based on Finite Fields and Euclidean Geometries

This letter presents an approach to the construction of non-binary low-density parity-check (LDPC) codes based on alpha-multiplied circulant permutation matrices and hyperplanes of two different…

Optimized geometric LDPC codes with quasi-cyclic structure

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...

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