  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.
