LDPC Codes Based on Rational Functions

Abstract

In this paper, some affine and rational functions are applied to define a class of LDPC codes, called RLDPC codes, which can be classified in two types, type-I and type-II, depending on being equivalent or not with APM-LDPC codes, respectively. Then, for each type, some explicit methods are provided to generate RLDPC codes with girth at least 6. While, cyclotomic cosets are used to generate type-I RLDPC codes, normal and diameter RLDPC codes are proposed as a class of type-II RLDPC codes which are analyzed for the existence of 4-cycles. Finally, simulation results show that the constructed type-II RLDPC codes outperform the randomly constructed QC LDPC codes, APM-LDPC codes and the LDPC codes based on PEG.

Keywords:

• Linear codes
• Parity check codes
• Error correction codes
• Matrices
• Bipartite graph
• Performance analysis

Acknowledgments

The authors would like to thank the anonymous referees for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the research council of Shahrekord University.

Notes on contributors

Mohammad Gholami

Mohammad Gholami was born on 27 July 1979, Isfahan, Iran, received the MS degree in mathematics in 2003 from Sharif University of Technology, Tehran, Iran, and the PhD degree in mathematics (Coding Theory) in 2009 form Isfahan University of Technology, Isfahan, Iran. His research interest includes algebraic coding theory, LDPC codes and iterative decoding algorithms. Since September 2009 he has been with the Department of Mathematical Sciences at Shahrekord University, Shahrekord, Iran, where he is now an associate professor. Corresponding author Email: [email protected]; [email protected]

Akram Nassaj

Akram Nassaj was born in Iran, she received the BE degree in mathematics from Kashan University of Iran and ME degree in mathematics from Sharif University of Technology of Tehran. She is now a doctor candidate of coding. Her research interests include LDPC codes. Email: [email protected].