Physics-Aware Decoding for Communication Channels Governed by Partial Differential Equations

TL;DR

This paper presents a novel physics-aware decoding framework that integrates PDE-based channel models with gradient descent algorithms, significantly improving error correction in physical media governed by PDEs.

Contribution

It introduces gradient flow decoding using differentiable PDE solvers, pioneering a new paradigm for physics-aware signal processing in communication systems.

Findings

Enhanced decoding performance on heat and NLSE equations

Demonstrated the effectiveness of PDE-integrated error correction

Established a new approach for physics-aware signal processing

Abstract

Digital communication systems inherently operate through physical media governed by partial differential equations (PDEs). In this paper, we introduce a physics-aware decoding framework that integrates gradient descent-based error correcting algorithms with PDE-based channel modeling using differentiable PDE solvers. At the core of our approach is gradient flow decoding, which harnesses gradient information directly from the PDE solver to guide the decoding process. We validate our method through numerical experiments on both the heat equation and the nonlinear Schr\"odinger equation (NLSE), demonstrating significant improvements in decoding performance. The implications of this work extend beyond decoding applications, establishing a new paradigm for physics-aware signal processing that shows promise for various signal detection and signal recovery tasks.