On the existence of typical minimum distance for protograph-based LDPC codes

Shadi Abu-Surra, Dariush Divsalar, William E. Ryan
2010 2010 Information Theory and Applications Workshop (ITA)  
In this paper we prove that, for a certain class of protograph-based LDPC codes with degree-two variable nodes, a typical minimum distance exists. We obtain a tight bound on the sum of weight enumerators, up to some weight d * , for the ensemble of finite-length protograph LDPC codes. Then we prove that this sum goes to zero as the block length goes to infinity. Finally, we prove that Pr(d < d * ) goes to zero as the block length goes to infinity. This typical minimum distance exists if
more » ... e exists if degreetwo nodes have certain connections to the check nodes. This is also important in practice since it identifies a certain class of protograph LDPC codes that have typical minimum distances.
doi:10.1109/ita.2010.5454136 dblp:conf/ita/Abu-SurraDR10 fatcat:wn2ciu7r7na7fneoqgk2tg3rui