Irregular repeat accumulate low-density parity-check codes based on residue class pair

This paper presents a new family of irregular repeat accumulate (IRA) low-density parity-check (LDPC) codes with the characteristic of random-like structure, a common feature of the practical LDPC codes adopted in most communication industrial standards. The systematic IRA-LDPC codes are defined by the parity-check matrix H = [H
^d
H
^P
], in which H
^d
and H
^P
correspond to the information bits and the parity bits respectively. We introduce the concept of residue class to create the residue class pair (RCP), from which we construct a compact representation of H
^d
matrix. It is demonstrated that, the family of designed RCP-based IRA-LDPC codes can provide better performance, higher structural level and lower memory consumption than the practical LDPC codes in some communication standards such as IEEE 802.16e and DVB-SII.