Column-Weight Three QC LDPC Codes with Girth 20

In this paper, some well-structured block designs are presented whose incidence matrices can be considered as the mother matrices of some regular and irregular column-weight three quasi cyclic low-density parity-check codes of girth 20. The class of LDPC codes derived from our construction possesses much more flexibility in terms of code length and rate. Moreover, the length of the regular constructed codes with rate at most 0.5 is at least 4.9 times smaller than the length of the voltage graph LDPC codes with the same rate and girth. Simulation results show that the constructed codes outperform progressive edge growth, repeat accumulate and random LDPC codes.

[1]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[2]  D.J.C. MacKay,et al.  Good error-correcting codes based on very sparse matrices , 1997, Proceedings of IEEE International Symposium on Information Theory.

[3]  Richard D. Wesel,et al.  Selective avoidance of cycles in irregular LDPC code construction , 2004, IEEE Transactions on Communications.

[4]  Emre Telatar,et al.  Finite-length analysis of low-density parity-check codes on the binary erasure channel , 2002, IEEE Trans. Inf. Theory.

[5]  Mohammad Gholami,et al.  Design of Binary and Nonbinary Codes from Lifting of Girth-8 Cycle Codes with Minimum Lengths , 2013, IEEE Communications Letters.

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

[7]  David Pask,et al.  Voltage Graphs , 2007 .

[8]  X. Jin.  Factor graphs and the Sum-Product Algorithm , 2002 .

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

[10]  Thomas J. Richardson,et al.  Error Floors of LDPC Codes , 2003 .

[11]  Evangelos Eleftheriou,et al.  Regular and irregular progressive edge-growth tanner graphs , 2005, IEEE Transactions on Information Theory.

[12]  T. Etzion,et al.  Which codes have cycle-free Tanner graphs? , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[13]  Dariush Divsalar,et al.  Coding theorems for 'turbo-like' codes , 1998 .

[14]  Robert Michael Tanner,et al.  A recursive approach to low complexity codes , 1981, IEEE Trans. Inf. Theory.

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

[16]  Sunghwan Kim,et al.  Quasi-Cyclic Low-Density Parity-Check Codes With Girth Larger Than $12$ , 2007, IEEE Transactions on Information Theory.