Quasicyclic low density parity check codes

In this work, the construction of low density parity check codes (LDPCs) from circulant permutation matrices is investigated. It is shown that such codes can not have a Tanner graph representation with girth larger than 12, and a relatively loose necessary and sufficient condition for the code to have a girth of 6, 8, 10 or 12 is derived. These results suggest that families of LDPC codes with such girth values are relatively easy to obtain and consequently, additional parameters such as the minimum distance or the number of redundant check sums should be considered.