With the surge of ubiquitous demand for high-complexity and quality mobile Internet-of-things (IoT) services, new cooperative relaying paradigms have emerged. Motivated by the long and unpredictable end-to-end communication in relay-aided IoT networks, there is a need to introduce novel modulation schemes for very low bit error rate (BER) communications. In this paper, a practical modulation mapping scheme has been proposed to reduce decoding errors. Specifically, a hybrid automatic repeat request (HARQ) system has been used with an intermediate relay to transfer a message from a source to a destination. The design of modulation mapping has been optimized by first formulating the objective as the quadratic assignment problem. Later, the solution to the mapping problem is provided using an iterative search method. To validate the proposed solution, extensive simulations have been performed in MATLAB. The results show that the proposed solution outperforms the conventional relay retransmission and the heuristic design approaches.