High performance non-binary quasi-cyclic LDPC codes on euclidean geometries

  • Authors:
  • Bo Zhou;Jingyu Kang;Ying Yu Tai;Shu Lin;Zhi Ding

  • Affiliations:
  • Qualcomm Inc., San Diego, CA and Department of Electrical and Computer Engineering, University of California at Davis, Davis, CA;Department of Electrical and Computer Engineering, University of California at Davis, Davis, CA;Boeing Company, El Segundo, CA and Department of Electrical and Computer Engineering, University of California at Davis, Davis, CA;Department of Electrical and Computer Engineering, University of California at Davis, Davis, CA;Department of Electrical and Computer Engineering, University of California at Davis, Davis, CA

  • Venue:
  • IEEE Transactions on Communications
  • Year:
  • 2009

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Abstract

This paper presents algebraic methods for constructing high performance and efficiently encodable non-binary quasi-cyclic LDPC codes based on flats of finite Euclidean geometries and array masking. Codes constructed based on these methods perform very well over the AWGN channel. With iterative decoding using a Fast Fourier Transform based sum-product algorithm, they achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision Berlekamp-Massey algorithm or algebraic soft-decision Kötter-Vardy algorithm. Due to their quasi-cyclic structure, these non-binary LDPC codes on Euclidean geometries can be encoded using simple shift-registers with linear complexity. Structured non-binary LDPC codes have a great potential to replace Reed-Solomon codes for some applications in either communication or storage systems for combating mixed types of noise and interferences.