  Approximate message passing (AMP) algorithms are iterative methods for signal
recovery in noisy linear systems. In some scenarios, AMP algorithms need to
operate within a distributed network. To address this challenge, the
distributed extensions of AMP (D-AMP, FD-AMP) and orthogonal/vector AMP
(D-OAMP/D-VAMP) were proposed, but they still inherit the limitations of
centralized algorithms. In this letter, we propose distributed memory AMP
(D-MAMP) to overcome the IID matrix limitation of D-AMP/FD-AMP, as well as the
high complexity and heavy communication cost of D-OAMP/D-VAMP. We introduce a
matrix-by-vector variant of MAMP tailored for distributed computing. Leveraging
this variant, D-MAMP enables each node to execute computations utilizing
locally available observation vectors and transform matrices. Meanwhile, global
summations of locally updated results are conducted through message interaction
among nodes. For acyclic graphs, D-MAMP converges to the same mean square error
performance as the centralized MAMP.
