Two Algebraic Methods for Constructing Efficiently Encodable Quasi-Cyclic LDPC Codes

摘要

In this paper, we present two algebraic methods for constructing Quasi-Cyclic LDPC codes. The first method is based on the quadratic residues modulo p (where p is a prime), the second method is based on the multiplicative inverses in finite fields. The codes constructed based on these methods are efficiently encodable and have a girth at least 6. Simulation results show that with SPA decoding, the constructed codes based on our methods perform very well over the AWGN channel compared to some other types of famous codes, such as random Mackay code or extended EG-LDPC code recommended by NASA.