🤖 AI Summary
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.
📝 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.