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Large communication networks, e.g. Internet of Things (IoT), are known to be vulnerable to co-channel interference. One possibility to address this issue is the use of orthogonal multiple access (OMA) techniques. However, due to a potentially very long duty cycle, OMA is not well suited for such schemes. Instead, random medium access (RMA) appears more promising. An RMA scheme is based on transmission of short data packets with random scheduling, which is typically unknown to the receiver. The received signal, which consists of the overlapping packets, can be used for energy harvesting and powering of a relay device. Such an energy harvesting relay may utilize the energy for further information processing and uplink transmission. In this paper, we address the design of a simultaneous information and power transfer scheme based on randomly scheduled packet transmissions and reliable symbol detection. We formulate a prediction problem with the goal to maximize the harvested power for an RMA scenario. In order to solve this problem, we propose a new prediction method, which shows a significant performance improvement compared to the straightforward baseline scheme. Furthermore, we investigate the complexity of the proposed method and its vulnerability to imperfect channel state information.