  Distribution-preserving integrated sensing and communication with secure
reconstruction is investigated in this paper. In addition to the distortion
constraint, we impose another constraint on the distance between the
reconstructed sequence distribution and the original state distribution to
force the system to preserve the statistical property of the channel states. An
inner bound of the distribution-preserving capacity-distortion region is
provided with some capacity region results under special cases. A numerical
example demonstrates the tradeoff between the communication rate,
reconstruction distortion and distribution preservation. Furthermore, we
consider the case that the reconstructed sequence should be kept secret from an
eavesdropper who also observes the channel output. An inner bound of the
tradeoff region and a capacity-achieving special case are presented.
