Low-Complexity and Piecewise Systematic Encoding of Non-Full-Rank QC-LDPC Codes

In this letter, we present a low-complexity encoding method for quasi-cyclic (QC) low-density parity-check (LDPC) codes in the case of non-full-rank parity-check matrices. Gaussian elimination can achieve systematic encoding, but it is usually too complex to implement. For QC-LDPC codes, efficient encoding methods have been presented by using shift-registers, but the encoded codewords are not systematic when parity-check matrices are non-full-rank. However, a systematic structure is important in practice. Therefore, we propose an encoding method which allows all information bits appear piecewise in the codeword, called piecewise systematic encoding.