Non-volatile memory reduction based on 1-D memory space mapping of a specific set of QC-LDPC codes

Supporting a great diversity of multi-rate H-matrices for multiple communication protocols requires a large amount of non-volatile memory, which may consume a large silicon area or logic elements and constrain the implementation of an overall decoder. Therefore, schemes for memory reduction are necessary to make the paritycheck storage more compact. This study proposes a specific set of quasi-cyclic low-density parity-check (LDPC) (QC-LDPC) codes which can transfer a traditional two-dimensional (2-D) parity-check matrix (H-matrix) into a onedimensional (1-D) memory space. Compared to the existing schemes, the proposed codes and memory reduction scheme do achieve significant reduction rates. Within a fixed memory space, many more H-matrices for diverse communication protocols can be saved via the proposed QC-LDPC codes, which are well constructed from modified Welch-Costas sequences. Furthermore, relatively good error performances, which outperform computergenerated random LDPC codes and Sridhara-Fuja-Tanner codes, are also shown in our simulation results. Consequently, we conclude that the proposed QC-LDPC codes can enlarge the capacity for saving much more low-BER (bit error rate) H-matrices within a fixed memory space.