This paper integrates mobile edge computing (MEC), non-orthogonal multiple access (NOMA), simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS), and wireless power transfer (WPT) to enhance the computational capabilities of Internet-of-Things(IoT) devices. A joint resource allocation problem is formulated to maximize the overall computation rate of two clusters of IoT devices. To address the non-convexity of the problem, we leverage semi-definite relaxation and bisection algorithms to obtain optimized amplitude and phase shifts of STAR-RIS, time, and power allocation for energy transfer and offloading. Numerical results show the necessity of phase shift optimization in STAR-RIS and the superiority of NOMA over its orthogonal multiple access counterpart in terms of total offloaded data size.
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