Distributed Vector Approximate Message Passing

This paper investigates distributed estimation problems with factorized structures over factor graphs. By building upon the recent progress in the approximate message passing (AMP) paradigm, this paper extends the vector AMP (VAMP) algorithm to the distributed scenario where multiple agents collaboratively estimate the same signal using different measurement channels. We do so by deriving the new collaborative linear minimum mean square error (LMMSE) messages within the estimation steps through message passing. The new algorithm — coined D-VAMP — allows distributed agents to be heterogeneous thereby handling a broader class of practical applications. Our numerical results demonstrate the trade-off between the reconstructed accuracy and the level of heterogeneity measured in terms of the number of correlated agents and signal-to-noise ratio.