Low-complexity LDPC-convolutional codes based on cyclically shifted identity matrices

Abstract

In this study, a construction methodology for low-density parity-check convolutional codes (LDPC-CCs) ensembles based on cyclically shifted identity matrices is proposed. The proposed method directly generates the syndrome former matrices according to the specified code parameters and constraints i.e., code-rate, degree-distribution, constraint length, period and memory, in contrast to the majority of the available approaches that produce relevant error-correcting codes based on either block ones, protographs or spatially-coupled type of codes. Simulation results show that the constructed ensembles demonstrate advanced error-correcting capability of up to 0.2 dB in terms of frame-error and bit-error rates at the convergence region, when compared with the performance of error-correcting schemes adopted by various communication standards, with equivalent hardware complexity even at short codeword-lengths. Specifically, the constructed LDPC-CCs have been assessed against the corresponding error-correcting codes used in WiMAX and G.hn standards for wireless and wireline telecommunications, respectively.