Several Explicit Constructions for (3,L) QC-LDPC Codes with Girth at Least Eight

Some explicit constructions for exponent matrices which correspond to Tanner graphs with girth at least eight are proposed. From these results, for any row weight of L>3, (3,L) quasi-cyclic LDPC codes with girth at least eight are constructed for any circulant permutation matrix (CPM) size P>L(L+mod(L,2))/2.

[1]  Xinmei Wang,et al.  New quasi-cyclic LDPC codes with girth at least eight based on Sidon sequences , 2012, 2012 7th International Symposium on Turbo Codes and Iterative Information Processing (ISTC).

[2]  Xinmei Wang,et al.  Construction of Girth-Eight QC-LDPC Codes from Greatest Common Divisor , 2013, IEEE Communications Letters.

[3]  Florian Hug,et al.  Searching for Voltage Graph-Based LDPC Tailbiting Codes With Large Girth , 2011, IEEE Transactions on Information Theory.

[4]  Jingming Kuang,et al.  Novel Algebraic Constructions of Nonbinary Structured LDPC Codes over Finite Fields , 2008, 2008 IEEE 68th Vehicular Technology Conference.

[5]  Shu-Tao Xia,et al.  Structured non-binary LDPC codes with large girth , 2007 .

[6]  M. E. O'Sullivan,et al.  Algebraic construction of sparse matrices with large girth , 2006, IEEE Transactions on Information Theory.

[7]  Xiaohu You,et al.  A necessary and sufficient condition for determining the girth of quasi-cyclic LDPC codes , 2008, IEEE Transactions on Communications.

[8]  Kyeongcheol Yang,et al.  A combining method of quasi-cyclic LDPC codes by the Chinese remainder theorem , 2005, IEEE Communications Letters.

[9]  M. Esmaeili,et al.  Structured quasi-cyclic LDPC codes with girth 18 and column-weight J⩾3 , 2010 .

[10]  Wuyang Zhou,et al.  Large-Girth Nonbinary QC-LDPC Codes of Various Lengths , 2010, IEEE Transactions on Communications.

[11]  Sunghwan Kim,et al.  On the girth of tanner (3, 5) quasi-cyclic LDPC codes , 2006, IEEE Transactions on Information Theory.

[12]  Baoming Bai,et al.  Construction of nonbinary quasi-cyclic LDPC cycle codes based on singer perfect difference set , 2010, IEEE Communications Letters.

[13]  Moon Ho Lee,et al.  Large Girth Non-Binary LDPC Codes Based on Finite Fields and Euclidean Geometries , 2009, IEEE Signal Processing Letters.

[14]  Marc P. C. Fossorier,et al.  Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices , 2004, IEEE Trans. Inf. Theory.

[15]  Bane V. Vasic,et al.  High-rate girth-eight low-density parity-check codes on rectangular integer lattices , 2004, IEEE Transactions on Communications.

[16]  Jen-Fa Huang,et al.  Construction of One-Coincidence Sequence Quasi-Cyclic LDPC Codes of Large Girth , 2012, IEEE Transactions on Information Theory.