A Framework for Learning and Reliability Certification in Neural Polar Decoding

Abstract

This paper investigates a framework that connects network training, independently certified population risk and sequential reliability in neural polar decoding. Network outputs determine information-bit decisions by their signs. Posterior mean-squared error (MSE) controls bit-error rate (BER), and a first-error identity connects errors evaluated with true preceding bits to sequential block-error rate (BLER). Three methods exploit sequential decoding structure to certify changes to trained receivers. First, distances from trained outputs to the zero decision threshold, termed learned margins, yield reliability bounds for over-parameterized neural network (ONN) updates subject to separate mean-squared output-change constraints at information positions. Second, a shared loss takes the largest block-error indicator difference between candidate decoders and successive cancellation (SC) on each frame. Its expectation bounds the corresponding BLER differences, termed excess BLER, for all fixed combinations of information-position implementations. An exact expression quantifies the gap between this shared bound and the largest BLER difference among fixed decoders. Third, verified linear programming (LP) and candidate-set subdivision tighten these guarantees with controllable computation at fixed confidence. ONN experiments assess conditional fitting and weight updates. Polar factor-graph experiments demonstrate reusable combination guarantees and storage reduction under prescribed excess-BLER allowances. Component timing identifies the dominant graph-propagation cost.