Physical unclonable functions (PUFs) produce responses by exploiting randomness that intrinsically occurs in integrated circuits due to uncontrollable variations in the manufacturing process of physical items. It is common practice that PUFs generate binary responses. Recently, it has been proposed to extract symbols from a higher-order alphabet in order to increase the length of the final response. In this paper, coding for this concept of multi-valued PUFs (MV-PUFs) is derived from the analogy to pulse-amplitude modulation in digital communications. To that end, based on ROPUF measurement data, we replace the classical binary symmetric channel model by a suited additive white Gaussian noise model. Consequently, the hard-input binary channel coding scheme is replaced by methods from coded modulation, utilizing the soft output. In addition, the functionality of helper data, which are required to stabilize noisy PUF responses, is transferred to the multi-valued case. By applying the designed methods to the available measurement data we eventually show that imagining the analog PUF output as $M$ -ary amplitude-shift keying symbols observed over an AWGN channel, both the extracted entropy per response symbol and the reliability of the final key can be increased.