Maximum-girth slope-based quasi-cyclic (2, k>=5) low-density parity-check codes

A class of maximum-girth geometrically structured regular (n,2,k5) (column-weight 2 and rowweightk) quasi-cyclic low-density parity-check (LDPC) codes is presented. The method is based on cylinder graphs and the slope concept. It is shown that the maximum girth achieved by these codes is 12. A lowcomplexity algorithm producing all such maximum-girth LDPC codes is given. The shortest constructed code has a length of 105. The minimum lengthnof a regular (2,k) LDPC code with girth g¼12 determined by the Gallager bound has been achieved by the constructed codes. From the perspective of performance these codes outperform the column-weight 2 LDPC codes constructed by the previously reported methods. These codes can be encoded using an erasure decoding process

girth, LDPC codes