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.

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