Physics-Aware Decoding for Communication Channels Governed by Partial Differential Equations
To address the low decoding efficiency and poor recovery accuracy of digital signals in physical channels governed by partial differential equations (PDEs)—such as heat conduction and the nonlinear Schrödinger equation (NLSE) channel—this paper proposes a physics-aware decoding framework. The core method introduces a novel gradient-flow decoding mechanism: leveraging backpropagated gradients from a differentiable PDE solver to directly guide iterative error correction, jointly optimizing channel modeling and symbol recovery under strict PDE constraints. Unlike conventional black-box neural networks or purely numerical solvers, our approach establishes a new signal processing paradigm grounded in physics-driven modeling and gradient-based optimization. Experiments on heat equation and NLSE channels demonstrate significantly reduced bit error rates, along with superior robustness and generalization compared to baseline methods. This work provides a differentiable, interpretable, and broadly applicable decoding pathway for physical-layer communications.