The problem of bistatic integrated sensing and communications over memoryless relay channels is considered, where destination concurrently decodes the message sent by the source and estimates unknown parameters from received signals with the help of a relay. A state-dependent discrete memoryless relay channel is considered to model this setup, and the fundamental limits of the communication-sensing performance tradeoff are characterized by the capacity-distortion function. An upper bound on the capacity-distortion function is derived, extending the cut-set bound results to address the sensing operation at the destination. A hybrid-partial-decode-and-compress-forward coding scheme is also proposed to facilitate source-relay cooperation for both message transmission and sensing, establishing a lower bound on the capacity-distortion function. It is found that the hybrid-partial-decode-and-compress-forward scheme achieves optimal sensing performance when the communication task is ignored. Furthermore, the upper and lower bounds are shown to coincide for three specific classes of relay channels. Numerical examples are provided to illustrate the communication-sensing tradeoff and demonstrate the benefits of integrated design.

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