A memoryless state-dependent multiple access channel is considered to model an integrated sensing and communication system, where two transmitters wish to convey messages to a receiver while simultaneously estimating the sensing state sequences through echo signals. In particular, the sensing states are assumed to be correlated with the channel state, and the receiver has imperfect channel state information. In this setup, improved inner and outer bounds for capacity-distortion region are derived. The inner bound is based on an achievable scheme that combines message cooperation and joint compression via distributed Wyner-Ziv coding at each transmitter, resulting in unified cooperative communication and sensing. The outer bound is based on the ideas of dependence balance for communication rate and rate-limited constraints on sensing distortion. The proposed inner and outer bounds are proved to improve the state-of-the-art bounds. Finally, numerical examples are provided to demonstrate that our new inner and outer bounds strictly improve the existing results.

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