On the Convergence of Orthogonal/Vector AMP: Long-Memory Message-Passing Strategy

This paper proves the convergence of Bayes-optimal orthogonal/vector approximate message-passing (AMP) to a fixed point (FP) in the large system limit. The proof is based on Bayes-optimal long-memory (LM) message-passing (MP) that converges in principle. The dynamics of Bayes-optimal LM-MP is analyzed via an existing state evolution framework. The obtained state evolution recursions are proved to converge. The convergence of Bayes-optimal orthogonal/vector AMP is proved by confirming an exact reduction of the state evolution recursions to those for Bayes-optimal orthogonal/vector AMP.