Jointly designed quasi-cyclic LDPC-coded cooperation with diversity combining at receiver

This correspondence proposes a jointly-designed quasi-cyclic (QC) low-density parity-check (LDPC)-coded multi-relay cooperation with a destination node realized by multiple receive antennas. First, a deterministic approach is utilized to construct different classes of binary QC-LDPC codes with no length-4 cycles. Existing methods put some limitations in terms of code length and rate in order to provide high error-correction performance. Therefore, this article gives three classes of QC-LDPC codes based on a combinatoric design approach, known as cyclic difference packing (CDP), with flexibility in terms of code-length and rate selection. Second, the proposed CDP-based construction is utilized to jointly-design QC-LDPC codes for coded-relay cooperation. At the receiver, the destination node is realized by multiple receive antennas, where maximal-ratio combining (MRC) and sum-product algorithm (SPA)-based joint iterative decoding are utilized to decode the corrupted sequences coming from the source and relay nodes. Simulation results show that the proposed QC-LDPC coded-relay cooperations outperform their counterparts with a coding gain of about 0.25 dB at bit-error rate (BER) 10 − 6 over a Rayleigh fading channel in the presence of additive white Gaussian noise. Furthermore, the extrinsic-information transfer (EXIT) chart analysis has been used to detect the convergence threshold of proposed jointly-designed QC-LDPC codes. Numerical analysis shows that the proposed jointly-designed QC-LDPC codes provide a better convergence as compared to their counterparts under the same conditions.