On the construction of LDPC convolutional code ensembles based on permuted circulant unit matrices

In this paper, a construction methodology for ensembles of Low-Density Parity-Check Convolutional Codes (LDPC-CCs) based on permuted circulant unit matrices is proposed. The proposed method directly generates the syndrome former matrices according to specified code parameters and constraints i.e. code-rate, degree-distribution, constraint length, period and memory, in contrast to the majority of the available methodologies 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 0.5 dB in terms of frame-error and bit-error rates at the convergence region, when compared to the performance of Forward Error Correction schemes adopted by various wireless standards, with comparable hardware complexity even at short codeword-lengths.