Construction of regular quasi cyclic-low density parity check codes from cyclic codes

Low Density Parity Check Codes (LDPC) are a class of linear error-correcting codes which have shown ability to approach or even to reach the capacity of the transmission channel. This class of code approaches asymptotically the fundamental limit of information theory more than the Turbo Convolutional codes. It's ideal for long distance transmission satellite, mobile communications and it's also used in storage systems. In this paper, a new method for constructing quasicyclic low density parity-check (QC-LDPC) codes derived from cyclic codes is presented. The proposed method reduces the incidence vectors, by eliminating the conjugates lines in parity-check matrix of the derived cyclic code to construct circulant shifting sub-matrices. In the end, this method produces a large class of regular LDPC codes of quasi-cyclic structure having very low density, high coding rates and Tanner graphs which have no short cycles with girth of at least 6. Performance with computer simulations are also shown in this work for some constructed codes. © 2006-2018 Asian Research Publishing Network (ARPN).