  In this paper, the `Approximate Message Passing' (AMP) algorithm, initially
developed for compressed sensing of signals under i.i.d. Gaussian measurement
matrices, has been extended to a multi-terminal setting (MAMP algorithm). It
has been shown that similar to its single terminal counterpart, the behavior of
MAMP algorithm is fully characterized by a `State Evolution' (SE) equation for
large block-lengths. This equation has been used to obtain the rate-distortion
curve of a multi-terminal memoryless source. It is observed that by spatially
coupling the measurement matrices, the rate-distortion curve of MAMP algorithm
undergoes a phase transition, where the measurement rate region corresponding
to a low distortion (approximately zero distortion) regime is fully
characterized by the joint and conditional Renyi information dimension (RID) of
the multi-terminal source. This measurement rate region is very similar to the
rate region of the Slepian-Wolf distributed source coding problem where the RID
plays a role similar to the discrete entropy.
  Simulations have been done to investigate the empirical behavior of MAMP
algorithm. It is observed that simulation results match very well with
predictions of SE equation for reasonably large block-lengths.
