Novel algorithm to construct QC-LDPC codes for high data rate applications

A novel algorithm to construct highly sparse, quasi-cyclic low-density parity check codes with large girth and high code rates that can be employed in high data rate applications is proposed. In this paper, a sparse girth six base matrix is designed, which is then substituted by a difference exponent matrix derived from a basic exponent matrix based on the powers of a primitive element in a finite field Fq, to build long code-length and high code rate QC-LDPC codes. The proposed exponent matrix generation is a one-time procedure and hence, less number of computations is involved. According to the simulation results, the proposed QC-LDPC code with high code rate showed faster encoding-decoding speeds and reduced storage overhead compared to conventional LDPC, conventional QC-LDPC codes, and traditional RS codes. Simulation results showed that the QC-LDPC codes constructed using the proposed algorithm performed very well over AWGN channel. Hardware implementation of the proposed high rate QC-LDPC code (N = 1248, R = 0.9) in Software Defined Radio platform using the NI USRP 2920 hardware device displays very low bit error rates compared to conventional QC-LDPC codes and conventional LDPC codes of similar size and rate. Thus, from both the simulation and hardware implementation results, the proposed QC-LDPC codes with high code rate were found to be suitable for high data rate applications such as cloud data storage systems and 5G wireless communication systems.