  In this paper, we establish achievable rate regions for the multiple access
channel (MAC) with side information partially known (estimated or sensed
version) at the transmitters. Actually, we extend the lattice strategies used
by Philosof-Zamir for the MAC with full side information at the transmitters to
the partially known case. We show that the sensed or estimated side information
reduces the rate regions, the same as that occurs for Costa Gaussian channel.
