Construction of LDPC codes based on resolvable group divisible designs

In this paper, we present a method for constructing LDPC codes from resolvable group divisible designs (RGDDs). According to the incidence matrices (or their submatrices) of RGDDs, a class of regular LDPC codes can be constructed. Since the parity-check matrix of the resulting code satisfies the row-column constraint, the girth of the proposed codes is at least six. Furthermore, based on a resolvable group divisible design, we can obtain a sequence of LDPC codes with various lengths and rates, which perform well over the AWGN channel with iterative decoding and have low error floors.

[1]  Bahram Honary,et al.  New constructions of quasi-cyclic LDPC codes based on special classes of BIDBs for the AWGN and binary erasure channels , 2007, IEEE Trans. Commun..

[2]  Bane V. Vasic,et al.  Combinatorial constructions of low-density parity-check codes for iterative decoding , 2002, IEEE Transactions on Information Theory.

[3]  Alan Hartman,et al.  Resolvable group divisible designs with block size 3 , 1989, Discret. Math..

[4]  Malcolm Greig.  Designs from projective planes and PBD bases , 1999 .

[5]  Shu Lin,et al.  Low-density parity-check codes based on finite geometries: A rediscovery and new results , 2001, IEEE Trans. Inf. Theory.

[6]  William Ryan,et al.  Channel Codes by William Ryan , 2009 .

[7]  Sarah J. Johnson,et al.  Construction of low-density parity-check codes from Kirkman triple systems , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[8]  Shu Lin,et al.  Iterative decoding of one-step majority logic deductible codes based on belief propagation , 2000, IEEE Trans. Commun..

[9]  H. Vincent Poor,et al.  Channel Coding Rate in the Finite Blocklength Regime , 2010, IEEE Transactions on Information Theory.

[10]  Khaled A. S. Abdel-Ghaffar,et al.  A unified approach to the construction of binary and nonbinary quasi-cyclic LDPC codes based on finite fields , 2009, IEEE Transactions on Communications.

[11]  David J. C. MacKay,et al.  Encyclopedia of Sparse Graph Codes , 1999 .

[12]  Radford M. Neal,et al.  Near Shannon limit performance of low density parity check codes , 1996 .

[13]  Xiuling Shan,et al.  A construction of low-density parity-check codes , 2013 .

[14]  Clement W. H. Lam,et al.  Resolvable group divisible designs with block size four and group size six , 2003, Discret. Math..

[15]  Khaled A. S. Abdel-Ghaffar,et al.  Algebraic Quasi-Cyclic LDPC Codes: Construction, Low Error-Floor, Large Girth and a Reduced-Complexity Decoding Scheme , 2014, IEEE Transactions on Communications.

[16]  Qiuju Diao,et al.  LDPC Codes on Partial Geometries: Construction, Trapping Set Structure, and Puncturing , 2013, IEEE Transactions on Information Theory.

[17]  Gennian Ge,et al.  Resolvable group divisible designs with block size four and general index , 2009, Discret. Math..

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

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

[20]  William Ryan,et al.  Channel Codes: Classical and Modern , 2009 .

[21]  David Declercq,et al.  Design of cages with a randomized progressive edge-growth algorithm , 2008, IEEE Communications Letters.

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

[23]  Rüdiger L. Urbanke,et al.  Design of capacity-approaching irregular low-density parity-check codes , 2001, IEEE Trans. Inf. Theory.

[24]  Shu Lin,et al.  Channel Codes: Classical and Modern , 2009 .