Nonlinear Posterior-Mean Feedback Codes for AWGN Channels

2026-10-04

AI Summary

This study addresses the performance limitations of classical feedback codes and the lack of interpretability in deep learning-based approaches by proposing a posterior mean feedback coding framework. This framework integrates analytical characterizations with a minimal set of learnable parameters, combining nonlinear construction, posterior mean refinement, maximum a posteriori (MAP) decoding, and projection design to establish a high-performance, interpretable communication scheme that effectively enhances robustness under noisy feedback. Experimental results demonstrate that the proposed method significantly outperforms multiple baseline models at finite blocklengths. By relying on only a few learnable parameters to achieve strong reliability, this work successfully bridges theoretical rigor and practical efficacy.

Abstract

Feedback can improve the reliability of communication over additive white Gaussian noise (AWGN) channels. Classical feedback codes are interpretable but often rely on linear estimation, while deep-learned feedback codes can achieve strong performance but require many learned parameters and are difficult to interpret. In this work, we propose an interpretable posterior-mean feedback coding framework for AWGN channels with feedback. The proposed scheme uses posterior-mean refinement to construct nonlinear feedback codes under both noiseless passive feedback and noisy active feedback, with maximum a posteriori (MAP) decoding at the receiver. We further develop a projection-based design to improve robustness under noisy feedback and support larger message sizes. Numerical results show that the proposed schemes achieve strong finite-blocklength performance and outperform several analytical and learned feedback coding baselines, while using only a small number of learned design parameters.

Problem

• AWGN channels
• feedback coding
• posterior-mean
• interpretability
• finite-blocklength

Innovation

• Posterior-Mean Feedback
• Nonlinear Coding
• Interpretable Code
• AWGN Channels
• Projection-Based Design