Type-II Quasi-Cyclic LDPC Codes with Girth Eight from Sidon Sequence

In this work, we consider type-II quasi-cyclic LDPC codes with girth eight from a Sidon sequence. We first derive the necessary and sufficient conditions guaranteeing girth-eight type-II QC-LDPC codes. By combining these conditions and the concept of a Sidon sequence, two classes of type-II codes are subsequently proposed with girth up to eight. We discuss the distance upper bounds of the two classes of codes and show that the second class provides a larger distance upper bound. In particular, to the best of our knowledge, the second class we proposed yields the first algebraic construction for girth-eight type-II codes with rates larger than a half and distance upper bounds exceeding twelve. Via simulations, we show that the girth-eight type-II codes from the second class significantly outperform the existing CDF-based girth-eight type-II codes, and that they perform better than or almost identically to the randomly generated girth-eight quadr. congr. codes.