Overflow-Avoiding Memory AMP
Information Theory
2026-01-01 v1 Signal Processing
math.IT
Statistics Theory
Statistics Theory
Abstract
Approximate Message Passing (AMP) type algorithms are widely used for signal recovery in high-dimensional noisy linear systems. Recently, a principle called Memory AMP (MAMP) was proposed. Leveraging this principle, the gradient descent MAMP (GD-MAMP) algorithm was designed, inheriting the strengths of AMP and OAMP/VAMP. In this paper, we first provide an overflow-avoiding GD-MAMP (OA-GD-MAMP) to address the overflow problem that arises from some intermediate variables exceeding the range of floating point numbers. Second, we develop a complexity-reduced GD-MAMP (CR-GD-MAMP) to reduce the number of matrix-vector products per iteration by 1/3 (from 3 to 2) with little to no impact on the convergence speed.
Cite
@article{arxiv.2407.03898,
title = {Overflow-Avoiding Memory AMP},
author = {Shunqi Huang and Lei Liu and Brian M. Kurkoski},
journal= {arXiv preprint arXiv:2407.03898},
year = {2026}
}