Integrated Sensing and Communication (ISAC) systems have garnered significant attention due to their capability to simultaneously achieve efficient communication and environmental sensing. A fundamental problem is to characterize the performance tradeoff between sensing and communication. In this paper, we investigate a joint source--channel coding (JSCC) problem in an ISAC system, where the transmitter observes a source sequence and aims to communicate it to the receiver under a given distortion criterion over a memoryless state-dependent channel, while simultaneously estimating the channel state based on feedback signals. We first prove that when the source and channel state are independent, separate source and channel coding (SSCC) is optimal for general source-to-channel blocklength ratios. For correlated source--state pairs with equal source and channel blocklengths, we derive single-letter inner and outer bounds on the achievable region. We further exhibit an example in which joint coding strictly outperforms the SSCC benchmark, and the proposed inner and outer bounds match at the specified sensing-distortion and input-cost budgets.

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