Recursive construction of (J,L) QC LDPC codes with girth 6

‎In this paper‎, ‎a recursive algorithm is presented to generate some exponent matrices which correspond to Tanner graphs with girth at least 6‎. ‎For a J times L exponent matrix E‎, ‎the lower bound Q(E) is obtained explicitly such that (J,L) QC LDPC codes with girth at least 6 exist for any circulant permutation matrix (CPM) size m geq Q(E)‎. ‎The results show that the exponent matrices constructed with our recursive algorithm have smaller lowerbound than the ones proposed recently with girth 6‎.