Systematic Turbo-Polar, Turbo-LDPC-Polar and Turbo-LDPC Codes Based on Belief Propagation Decoding

In this paper, we propose the Turbo principle (of using parallel concatenated channel encoders separated by an interleaver and iterative soft-input and soft-output decoding between the constituent decoders) onto Polar and LDPC codes resulting in Turbo-Polar, Turbo-LDPC-Polar and Turbo-LDPC schemes with the aim of enhancing the BLER performance while also reducing the decoding complexity. All the proposed turbo-coded schemes are decoded using the traditional Belief Propagation (BP) algorithm based on low-density parity-check iterative decoding through a factor graph. Monte Carlo simulation results confirm the superiority of Turbo-LDPC and Turbo-LDPC-Polar schemes in BLER performance over state-of-the-art cyclic redundancy check-aided successive cancellation List decoding (CA-SCL) of Polar Codes with a large list size of 32 for large block lengths (larger than 3072 bits) while having reduced computational decoding complexity in comparison to CA-SCL decoding in an additive white Gaussian noise (A WGN) channel. Furthermore, Turbo-LDPC (based on 5G New Radio specifications for LDPC code) outperforms the standalone 5G-NR LDPC code and achieves about 1 dB gain at a BLER of 10–
⁴
over correlated slow fading Rayleigh channel; however, being turbo-iterative in nature, it has higher complexity (about six-fold) than the standalone 5GNR LDPC code.