A New Insight Into GAMP and AMP

Abstract

A concise expectation propagation (EP) based message passing algorithm (MPA) is derived for the general measurement channel. By neglecting some high-order infinitesimal terms, the EP-MPA is proven to be equivalent to the Generalized Approximate Message Passing (GAMP), which exploits central limit theorem and Taylor expansion to simplify the belief propagation process. Furthermore, for additive white gaussian noise measurement channels, EP-MPA is proven to be equivalent to the AMP. Such intrinsic equivalence between EP and GAMP/AMP offers a new insight into GAMP and AMP via a unified message passing rule for non-linear processing, and may provide clues towards building new MPAs in solving more general non-linear problems.

Grant-Free Access via Bilinear Inference for Cell-Free MIMO With Low-Coherence Pilots

“…These algorithms require, however, matrix inversion operations unlike the original AMP approach. A rigorous analysis of the convergence property of this approach was presented in [30], [33], and potential connection among different methods was investigated in [34]- [36], with the extension to the bilinear inference method proposed in [37], [38]. Also, it is worth-noting that the Gaussian belief propagation (GaBP) [8] approach can be interpreted as the origin of the aforementioned AMP-based message passing rules.…”

“…Total number of bits (36) where P 1 e denotes the number of errors due to failure of symbol detection and P 2 e is the number of bits that have been lost due to failure of user detection.…”

Parametric Bilinear Iterative Generalized Approximate Message Passing Reception of FTN Multi-Carrier Signaling

“…3, this message is calculated by integrating the product of the messages propagated from all VNs x q and h q to the FN p(z k,n |h q , x q ) and the function p(z k,n |h q , x q ) over all the VNs in x q and h q . Applying central-limit-theorem (CLT) to the messages gleaned from the FNs p(z q |h q , x q ) to the VNs zq , we can approximate the pseudo a priori probabilities of the noiseless measurements zq by independent Gaussian distributions having the mean vector of pq (t) and the variance vector of ν p q (t) [22]. The pseudo a priori variance vector ν p q (t) of the noiseless measurements zq in the t-th iteration is derived as…”

“…Compute ν p q (t) and pq (t) using ( 15) and ( 17). Compute ŝq (t) and ν s q (t) using ( 21) and (22).…”

An Enhanced Tabu Search Based Receiver for Full-Spreading NOMA Systems

“…The authors of [30]- [32] proved that the proposed schemes always converge to the LMMSE performance with low complexity. In [36], concise expectation propagation-based MPA (EP-MPA) was proposed as a way to solve non-linear problems more efficiently compared to the GMP algorithms. On the other hand, there has been active research work based on the AMP methods such as orthogonal AMP (OAMP) [37], vector AMP (VAMP) [38]- [40], and bilinear generalized AMP (BiGAMP) [38], [39], etc.…”