Quasi-cyclic LDPC codes with high girth

The LDPC codes are codes that approach optimal decoding performances, with an acceptable decoding computational cost ([1, 2, 3]). In this paper we present a class of quasi-cyclic LDPC codes and we show that we are able to guarantee some relevant properties of the codes. Experimentally, their decoding performance is comparable with the performance obtained by random LDPC codes. Traditionally, coding theory is divided into two main research areas: algebraic coding theory and probabilistic coding theory. The former ([4]) deals with codes endowed with a nice algebraic structure, which allows both to study their internal properties and to have efficient encoding-decoding techniques, the latter deals with convolutional codes, which are very difficult to study and randomly constructed,