New low-density parity-check codes with large girth based on hypergraphs

The relation between low-density parity-check (LDPC) codes and hypergraphs supports searching for powerful LDPC codes based on hypergraphs. On the other hand, coding theory methods can be used in searching for hypergraphs with large girth. Moreover, compact representations of hypergraphs based on convolutional codes can be found. Algorithms for iteratively constructing LDPC codes with large girth and for determining their minimum distance are introduced. New quasi-cyclic (QC) LDPC codes are presented, some having both optimal girth and optimal minimum distance.