An approach to evaluating the number of potential cycles in an all-one base matrix

The 'Tree Method' is usually used to identify potential cycles in low-density parity-check codes. However, with the increasing demand of high girth codes, the method becomes hard to implement because of the exponential increase of both space complexity and time complexity. In this paper, a new method is introduced to evaluate potential cycles for all-one base matrix. The method applies to large cycle length and arbitrary size base matrix. The principle of potential cycle and potential cycle duplication are studied to support the new approach. Instead of doing low efficient exhaustive search, the approach gives the number of potential cycles without duplication directly. The results of cycle numbers are given, which are verified by the 'Tree Method'.