Construction of nonbinary quasi-cyclic LDPC cycle codes based on singer perfect difference set

Authors:
Chao Chen;Baoming Bai;Xinmei Wang
Affiliations:
State Key Lab. of ISN, Xidian University, Xi'an, China;State Key Lab. of ISN, Xidian University, Xi'an, China;State Key Lab. of ISN, Xidian University, Xi'an, China
Venue:
IEEE Communications Letters
Year:
2010

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Abstract

A low-density parity-check (LDPC) code whose parity-check matrix consists of weight-2 columns is known as a cycle code. In this letter, we propose a construction of nonbinary quasi-cyclic (QC) LDPC cycle codes based on Singer perfect difference set. The Tanner graph has girth 12 and the code length achieves the Gallager lower bound. We further show that constructed codes have exactly a minimum symbol Hamming distance 6. Simulation results show that the proposed codes perform better than random nonbinary LDPC cycle codes.