Approximate Message Passing for Bilinear Models

Approach: We take a Bayesian approach to the inference problems (in particular, posterior estimation) that revolve around the bilinear model (1). In particular, we leverage the approximate message passing (AMP) framework of [2], [3] and extend it to the bilinear domain. Compared to Bayesian approaches that rely on Gibbs sampling methods or variational inference, the AMP framework allows us to fully exploit the blessings-of-dimensionality (e.g., the asymptotic normality and concentration-of-measures) to achieve salient advantages in computation and estimation accuracy. Our “turbo AMP” framework also allows us to characterize the impact of our message scheduling using extrinsic information transfer (EXIT) charts, originally developed to predict the convergence of turbo decoding.