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This paper proposes a cooperative relay transmission exploiting a concatenated structure composed of a simple exclusive OR (XOR) network code and channel codes. A main contribution of this paper is to clarify the joint network-and-channel coding combined with an iterative decoding is effective in providing highly reliable wireless communications even in the case where distances from one destination node to two source nodes are not the same in the case of triangular topology network. In this case, it is subject to imbalanced signal powers at the destination node, resulting in imbalanced link quality. In this paper, we focus on an analogy between the triangular topology network and a quaternary PSK (QPSK) symbol with a rectangular shape, i.e., imbalanced the in-phase and quadrature-phase (I-Q). After demonstrating that the rectangular QPSK has a potential to detect signals with high accuracy by iterative decoding, a configuration of the cooperative relay to be proposed in this paper is revealed. Computer simulation confirms that both the rectangular QPSK and the cooperation are effective to solve the imbalanced problem.