An Unnoticed Property in QC-LDPC Codes to Find the Message from the Codeword in Non-Systematic Codes

• Published in: 2019 European Conference on Networks and Communications (EuCNC) pp. 6 - 9
• Main Authors: Hasani, Alireza, Lopacinski, Lukasz, Buchner, Steffen, Nolte, Jorg, Kraemer, Rolf
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-06-2019
• ISSN: 2575-4912
• DOI: 10.1109/EuCNC.2019.8801957

The generator matrix of quasi-cyclic low-density parity-check (QC-LDPC) codes is not, in general, in systematic form. Therefore, finding the message corresponding to a detected codeword at the receiver is not as straightforward as it is in the case of systematic codes. In this paper, we propose two methods for finding the message from the codeword in a QC-LDPC code. The first method is a general scheme which views the problem as a set of linear equations. This method is not realizable with pure digital circuits and may be implemented by having a processor core in the design. The second method is rather an alternative scheme which makes use of a particular structure in generator matrices of QC-LDPC codes in order to find the message from a non-systematic codeword. We examine a large class of non-systematic Latin squares QC-LDPC codes and one of the IEEE 802.16e standard QC-LDPC codes, and show that they have the required structure to be usable by the algorithm. The latter method is realizable in hardware and can be implemented with a digital circuit consisting of XOR gates.