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We develop an analytical framework to characterize the effect of impulsive noise on the performance of relay-assisted simultaneous wireless information and power transfer (SWIPT) systems. We derive novel closed-form expressions for the pairwise error probability (PEP) considering two variants based on the availability of channel state information (CSI), namely, blind relaying and CSI-assisted relaying. We further consider two energy harvesting (EH) techniques, i.e., instantaneous EH (IEH) and average EH (AEH). Capitalizing on the derived analytical results, we present a detailed numerical investigation of the diversity order for the underlying scenarios under the impulsive noise assumption. For the case when two relays and the availability of a direct link, it is demonstrated that the considered SWIPT system with blind AEH-relaying is able to achieve an asymptotic diversity order of less than 3, which is equal to the diversity order achieved by CSI-assisted IEH-relaying. This result suggests that, by employing the blind AEH relaying, the power consumption of the network can be reduced, due to eliminating the need of CSI estimation. This can be achieved without any performance loss. Our results further show that placing the relays close to the source can significantly mitigate the detrimental effects of impulsive noise. Extensive Monte Carlo simulation results are presented to validate the accuracy of the proposed analytical framework.