Analytical Lower Bounds on the Size of Elementary Trapping Sets of Variable-Regular LDPC Codes With Any Girth and Irregular Ones With Girth 8

In this paper, we give lower bounds on the size of (a, b) elementary trapping sets (ETSs) of variable-regular LDPC codes with any girth, g, and irregular ones with girth 8, where a is the size and b is the number of degree-one check nodes. Our proposed lower bounds are analytical, applicable to all values of g and b, based on graph theories and tighter than the existing ones in the literature. Our results mostly depend on the girth. We also propose results, which are independent of the girth and rely on the variables a, b, y, and the column weight value. We obtain the tightest lower bounds on the size of ETSs of variable-regular LDPC codes with girth eight. These results provide us with a chance to present a method to achieve the minimum size of ETSs of irregular LDPC codes with girth, especially those whose column weight values are a subset of (2, 3, 4, 5, 61 and fulfill the inequality (b/a) <; 1. Moreover, we present a range of numerical results about (a, b) ETSs with girths 8 and 10 to compare the tightness between our proposed lower bounds and the existing bounds in the literature.