Efficient encoding of quasi-cyclic low-density parity-check codes

• Published in: IEEE transactions on communications Vol. 54; no. 1; pp. 71 - 81
• Main Authors: Zongwang Li, Lei Chen, Lingqi Zeng, Lin, S., Fong, W.H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-01-2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Application software; Applied sciences; Array of circulants; Belief propagation; Circuits; Coding, codes; Computer errors; Encoding; Exact sciences and technology; Generators; High speed; Information, signal and communications theory; Iterative decoding; Mathematical analysis; Matrices; Matrix methods; NASA; Parity check codes; quasi-cyclic (QC) low-density parity-check (LDPC) codes; Serials; Shift registers; Signal and communications theory; Sparse matrices; systematic-circulant (SC) form; Telecommunications and information theory; Array of circulants; Cyclic code; systematic-circulant (SC) form; Bit error rate; Coding circuit; Data transmission; Parity check codes; Performance analysis; quasi-cyclic (QC) low-density parity-check (LDPC) codes
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2005.861667

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.