A physically unclonable function includes a circuit that translates a normally distributed sequence of raw sample into a sequence of uniformly distributed binned values across sub-bins of bins. Helper circuitry generates centering values and parity bits based on binned values generated during registration. Each centering value is associated with a raw sample value corresponding to a binned value and indicates an offset of a sub-bin in one of the bins. A distance calculator generates a set of distances from each raw sample value based on the centering value associated with the raw sample value. Each distance indicates a difference between the respective raw sample value and a raw sample value equivalent to a midpoint of a sub-bin offset by the associated centering value in a bin. A trellis decoder generates a PUF signature based on the candidate symbols, sets of distances, and parity bits.