A general performance analysis framework for bitwise neural polar decoding
This paper investigates when the population mean-squared error (MSE) of a bitwise neural predictor is sufficient to guarantee a bit-error rate (BER) close to the successive-cancellation (SC) reference performance. Each synthesized message channel is formulated as a soft maximum a posteriori (MAP) regression problem. Architecture-independent direct and posterior-margin MSE-to-BER bounds then convert certified population MSE into an SC-referenced reliability requirement, while an independent held-out certificate makes the population condition verifiable from data. A three-layer over-parameterized neural network (ONN) decoder, comprising an input layer, one over-parameterized rectified linear unit (ReLU) hidden layer, and a fixed-sign output layer, provides a constructive instance with provable empirical MSE convergence under explicit full-batch gradient-descent conditions. A (128,64) shared-message-update polar factor-graph neural decoder is further evaluated over additive white Gaussian noise (AWGN) and block-Rayleigh channels to examine architecture-independent certification and engineering performance. The resulting reliability-certification framework connects trainability, population regression accuracy, and communication reliability. It provides verifiable sufficient conditions for an SC-referenced BER guarantee and its associated block-error rate (BLER) characterization.