Recursive construction of (J,L) QC LDPC codes with girth ۶

‎In this paper‎, ‎a recursive algorithm is presented to generate some exponent matrices which correspond to Tanner graphs with girth at least ۶‎. ‎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 ۶ 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 lower-bound than the ones proposed recently with girth ۶‎.

Keywords:

‎QC LDPC codes‎ , ‎Tanner graph‎ , ‎exponent matrix