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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 …