Title :
Efficient encoding of quasi-cyclic low-density parity-check codes
Author :
Li, Zongwang ; Chen, Lei ; Zeng, Lingqi ; Lin, Shu ; Fong, Wai H.
Author_Institution :
Data Storage Syst. Center, Carnegie Mellon Univ., Pittsburgh, PA, USA
Abstract :
Quasi-cyclic (QC) low-density parity-check (LDPC) codes form an important subclass of LDPC codes. These codes have encoding advantage over other types of LDPC codes. This paper addresses the issue of efficient encoding of QC-LDPC codes. Two methods are presented to find the generator matrices of QC-LDPC codes in systematic-circulant (SC) form from their parity-check matrices, given in circulant form. Based on the SC form of the generator matrix of a QC-LDPC code, various types of encoding circuits using simple shift registers are devised. It is shown that the encoding complexity of a QC-LDPC code is linearly proportional to the number of parity bits of the code for serial encoding, and to the length of the code for high-speed parallel encoding.
Keywords :
matrix algebra; parity check codes; shift registers; LDPC codes; encoding circuits; encoding complexity; generator matrices; high-speed parallel encoding; parity bits; parity-check matrices; quasicyclic low-density parity-check codes; serial encoding; shift registers; systematic-circulant form; Application software; Belief propagation; Circuits; Computer errors; Encoding; Iterative decoding; NASA; Parity check codes; Shift registers; Sparse matrices; Array of circulants; quasi-cyclic (QC) low-density parity-check (LDPC) codes; systematic-circulant (SC) form;
Journal_Title :
Communications, IEEE Transactions on
DOI :
10.1109/TCOMM.2005.861667