Jointly optimized quasi-cyclic LDPC codes for coded-cooperative wireless networks based on split labeling diversity

This manuscript proposes the quasi-cyclic low-density parity-check (QC-LDPC) coded-cooperative scheme based on the split labeling diversity (QC-LDPCC-SLD) with a single antenna over the Rayleigh frequency-flat fast fading channel. The two grith-4 cycle-free QC-LDPC codes are employed in the source and relay, respectively. To cancel the cycles of length-4 in the cross-layer of the joint QC-LDPC codes obtained at the destination, a simple optimized approach is developed based on the bi-layer joint Tanner graph. In addition, 16-ary quadrature amplitude modulation (16-QAM) and 16-ary phase shift keying (16-PSK) are utilized in the proposed QC-LDPCC-SLD scheme, where the two distinct optimized labeling mappers of labeling diversity (LD) are split appropriately and equipped in the relay and source, respectively, therefore lowering the error-floor (EF) region. Moreover, the novel joint Turbo-Decoding Message-Passing iterative decoding algorithm is developed to further enhance the overall BER performance and reduce the decoding complexity. Theoretical analysis and numerical results demonstrate that the proposed QC-LDPCC-SLD scheme significantly outperforms the corresponding non-cooperative schemes by more than 3.4 dB and is closer to the EF bound at the high signal-to-noise rate. Moreover, the performance of the proposed QC-LDPCC-SLD scheme is improved by at least 16 % at a BER of the order of $$10^{-5}$$ 10 - 5 compared to the existing QC-LDPC counterpart systems.