Three-Module SC-VAMP for LDPC-Coded Nonlinear Channels

TL;DR

This paper introduces a modular three-module SC-VAMP algorithm for signal recovery in nonlinear channels, combining likelihood, coupling, and decoding modules for improved LDPC code performance.

Contribution

It presents a novel, adaptable three-module framework that efficiently handles nonlinear channels by decomposing the inference into specialized components with closed-form message updates.

Findings

Achieves a clear waterfall in bit error rate (BER) performance.

Narrowing gap to capacity as block length increases from 128 to 2304.

Modular architecture easily adaptable to various nonlinear channel models.

Abstract

We propose a three-module extension of score-based VAMP (SC-VAMP) for signal recovery in nonlinear channels, where the received signal is obtained by applying a nonlinearity to a linear mixture of the transmitted signal, followed by additive Gaussian noise. The key idea is to introduce a latent variable representing the output of the linear mixing stage, which decomposes the inference problem into three modules: a likelihood module that handles the nonlinear observation via Gauss--Hermite quadrature, a coupling module that enforces the linear constraint between the transmitted signal and the latent variable via LMMSE estimation, and a denoiser module that incorporates the code constraint using belief propagation (BP) decoding. Each module exchanges extrinsic scalar-Gaussian messages with Onsager corrections derived from posterior variances that are computed in closed form or to quadrature accuracy. Numerical experiments with BPSK-modulated LDPC codewords transmitted through a hyperbolic tangent channel demonstrate that the proposed method achieves a clear waterfall in bit error rate (BER), with the gap to the capacity estimate narrowing as the block length increases from 128 to 2304. The framework provides a modular receiver architecture applicable to a broad class of nonlinear channels. Since only the likelihood module depends on the channel nonlinearity, the architecture readily adapts to other channel models by replacing a single module while leaving the coupling and decoder modules unchanged.