Multi-Layer Bilinear Generalized Approximate Message Passing

TL;DR

This paper introduces ML-BiGAMP, a multi-layer extension of BiG-AMP, which efficiently approximates high-dimensional Bayesian inference in cascaded systems, with proven optimality and practical application in relay communication.

Contribution

The paper develops ML-BiGAMP, a novel multi-layer algorithm that reduces complexity and retains Bayes-optimal performance for high-dimensional bilinear problems.

Findings

ML-BiGAMP accurately predicts MMSE via state evolution.

ML-BiGAMP achieves near-optimal performance with lower computational cost.

Demonstrated effectiveness in relay communication channel estimation.

Abstract

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm called ML-BiGAMP could approximate the general sum-product loopy belief propagation (LBP) in the high-dimensional limit enjoying a substantial reduction in computational complexity. We demonstrate that, in large system limit, the asymptotic MSE performance of ML-BiGAMP could be fully characterized via a set of simple one-dimensional equations termed state evolution (SE). We establish that the asymptotic MSE predicted by ML-BiGAMP' SE matches perfectly the exact MMSE predicted by the replica method, which is well known to be Bayes-optimal but infeasible in practice. This consistency indicates that the ML-BiGAMP may still retain the same Bayes-optimal performance as the MMSE estimator in high-dimensional applications, although ML-BiGAMP's computational burden is far lower. As an illustrative example of the general ML-BiGAMP, we provide a detector design that could estimate the channel fading and the data symbols jointly with high precision for the two-hop amplify-and-forward relay communication systems.