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Shu Lin - One of the best experts on this subject based on the ideXlab platform.

  • quasi cyclic ldpc codes an algebraic construction
    IEEE Transactions on Communications, 2010
    Co-Authors: Jingyu Kang, Qin Huang, Li Zhang, Bo Zhou, Shu Lin
    Abstract:

    This paper presents two new large classes of QC-LDPC codes, one binary and one non-binary. Codes in these two classes are constructed by array dispersions of row-distance constrained matrices formed based on additive subgroups of Finite fields. Experimental results show that codes constructed perform very well over the AWGN channel with iterative decoding based on belief propagation. Codes of a subclass of the class of binary codes have large minimum distances comparable to Finite Geometry LDPC codes and they offer effective tradeoff between error performance and decoding complexity when decoded with low-complexity reliability-based iterative decoding algorithms such as binary message passing decoding algorithms. Non-binary codes decoded with a Fast-Fourier Transform based sum-product algorithm achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either the hard-decision Berlekamp-Massey algorithm or the algebraic soft-decision Kotter-Vardy algorithm. They have potential to replace Reed-Solomon codes in some communication or storage systems where combinations of random and bursts of errors (or erasures) occur.

  • construction of nonbinary cyclic quasi cyclic and regular ldpc codes a Finite Geometry approach
    IEEE Transactions on Communications, 2008
    Co-Authors: Lingqi Zeng, Bo Zhou, Shu Lin, Lan Lan, Ying Yu Tai, Khaled Abdelghaffar
    Abstract:

    This paper presents five methods for constructing nonbinary LDPC codes based on Finite geometries. These methods result in five classes of nonbinary LDPC codes, one class of cyclic LDPC codes, three classes of quasi-cyclic LDPC codes and one class of structured regular LDPC codes. Experimental results show 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 of the same lengths and rates with either algebraic hard-decision decoding or Kotter-Vardy algebraic soft-decision decoding at the expense of a larger decoding computational complexity.

  • dispersed reed solomon codes for iterative decoding and construction of q ary ldpc codes
    Global Communications Conference, 2005
    Co-Authors: Lingqi Zeng, Lan Lan, Ying Yu Tai, Shu Lin
    Abstract:

    This paper presents three algebraic methods for constructing q-ary LDPC codes. The first method gives a class of dispersed Reed-Solomon codes as LDPC codes. The second method gives a class of q-ary quasi-cyclic LDPC codes. The third method gives two classes of q-ary Finite Geometry LDPC codes. Codes constructed by these methods perform very well with iterative decoding, even for short codes.

  • low density parity check codes based on Finite geometries a rediscovery and new results
    IEEE Transactions on Information Theory, 2001
    Co-Authors: Yu Kou, Shu Lin, M P C Fossorier
    Abstract:

    This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over Finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-Geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-Geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended Finite-Geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.

M P C Fossorier - One of the best experts on this subject based on the ideXlab platform.

  • low density parity check codes based on Finite geometries a rediscovery and new results
    IEEE Transactions on Information Theory, 2001
    Co-Authors: Yu Kou, Shu Lin, M P C Fossorier
    Abstract:

    This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over Finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-Geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-Geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended Finite-Geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.

Dimitris A Pados - One of the best experts on this subject based on the ideXlab platform.

  • a decoding algorithm for Finite Geometry ldpc codes
    IEEE Transactions on Communications, 2005
    Co-Authors: Zhenyu Liu, Dimitris A Pados
    Abstract:

    In this paper, we develop a new low-complexity algorithm to decode low-density parity-check (LDPC) codes. The developments are oriented specifically toward low-cost, yet effective, decoding of (high-rate) Finite-Geometry (FG) LDPC codes. The decoding procedure updates iteratively the hard-decision received vector in search of a valid codeword in the vector space. Only one bit is changed in each iteration, and the bit-selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optional mechanism to avoid inFinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity for FG-LDPC codes.

Yu Kou - One of the best experts on this subject based on the ideXlab platform.

  • low density parity check codes based on Finite geometries a rediscovery and new results
    IEEE Transactions on Information Theory, 2001
    Co-Authors: Yu Kou, Shu Lin, M P C Fossorier
    Abstract:

    This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over Finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-Geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-Geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended Finite-Geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.

Bo Zhou - One of the best experts on this subject based on the ideXlab platform.

  • quasi cyclic ldpc codes an algebraic construction
    IEEE Transactions on Communications, 2010
    Co-Authors: Jingyu Kang, Qin Huang, Li Zhang, Bo Zhou, Shu Lin
    Abstract:

    This paper presents two new large classes of QC-LDPC codes, one binary and one non-binary. Codes in these two classes are constructed by array dispersions of row-distance constrained matrices formed based on additive subgroups of Finite fields. Experimental results show that codes constructed perform very well over the AWGN channel with iterative decoding based on belief propagation. Codes of a subclass of the class of binary codes have large minimum distances comparable to Finite Geometry LDPC codes and they offer effective tradeoff between error performance and decoding complexity when decoded with low-complexity reliability-based iterative decoding algorithms such as binary message passing decoding algorithms. Non-binary codes decoded with a Fast-Fourier Transform based sum-product algorithm achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either the hard-decision Berlekamp-Massey algorithm or the algebraic soft-decision Kotter-Vardy algorithm. They have potential to replace Reed-Solomon codes in some communication or storage systems where combinations of random and bursts of errors (or erasures) occur.

  • construction of nonbinary cyclic quasi cyclic and regular ldpc codes a Finite Geometry approach
    IEEE Transactions on Communications, 2008
    Co-Authors: Lingqi Zeng, Bo Zhou, Shu Lin, Lan Lan, Ying Yu Tai, Khaled Abdelghaffar
    Abstract:

    This paper presents five methods for constructing nonbinary LDPC codes based on Finite geometries. These methods result in five classes of nonbinary LDPC codes, one class of cyclic LDPC codes, three classes of quasi-cyclic LDPC codes and one class of structured regular LDPC codes. Experimental results show 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 of the same lengths and rates with either algebraic hard-decision decoding or Kotter-Vardy algebraic soft-decision decoding at the expense of a larger decoding computational complexity.