Efficient Encoding of Quasi-Cyclic Low-Density Parity-Check Codes

A compact encoding process with three phases is proposed for quasi-cyclic low-density parity-check (QC-LDPC) codes. A back substitution circuit is shared at the first and third phases. A high-speed vector-dense-matrix multiplier is well designed for the second phase, which offers tradeoffs between speed and memory. The proposed encoding method just removes some nonzero circulants of a sparse parity-check matrix $\pmb{H}$. while the classical Richardson-Urbanke (RU) approach splits $\pmb{H}$ into multiple submatrices and destroys its integrity. It is shown that the proposed encoder runs fast, has low complexity, and is well compatible with multiple code rates.