  In this paper, we consider the generation and utilization of helper data for
physical unclonable functions (PUFs) that provide real-valued readout symbols.
Compared to classical binary PUFs, more entropy can be extracted from each
basic building block (PUF node), resulting in longer keys/fingerprints and/or a
higher reliability. To this end, a coded modulation and signal shaping scheme
that matches the (approximately) Gaussian distribution of the readout has to be
employed. A new helper data scheme is proposed that works with any type of
coded modulation/shaping scheme. Compared to the permutation scheme from the
literature, less amount of helper data has to be generated and a higher
reliability is achieved. Moreover, the recently proposed idea of a two-metric
helper data scheme is generalized to coded modulation and a general S-metric
scheme. It is shown how extra helper data can be generated to improve
decodability. The proposed schemes are assessed by numerical simulations and by
evaluation of measurement data. We compare multi-level codes using a new rate
design strategy with bit-interleaved coded modulation and trellis shaping with
a distribution matcher. By selecting a suitable design, the rate per PUF node
that can be reliably extracted can be as high as 2~bit/node.
