ON THE DESIGN OF QUASI-CYCLIC LDPC CODES FROM ABELIAN S 2 -SETS

The main goal of this paper is to present a brief survey about the applica- tions of algebraic tools in different aspects of communications. As a special instance of such applications, we deal with the design of Quasi-cyclic (QC) low-density parity-check (LDPC) codes, which are also known as QC-LDPC codes. QC-LDPC codes have many applications due to their simple encoding implementation by means of cyclic shift reg- isters. In this paper, we present the construction of QC-LDPC codes from S 2 -sets in Abelian groups. Some of the previously addressed methods for constructing QC-LDPC codes based on finite fields and cyclic difference sets are special cases of the proposed construction method.