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In this work, we consider $q$-ary signature codes of length $k$ and size $n$ for a noisy adder multiple access channel. A signature code in this model has the property that any subset of codewords can be uniquely reconstructed based on any vector that is obtained from the sum (over integers) of these codewords. We show that there exists an algorithm to construct a signature code of length $k = \frac{2n\log{3}}{(1-2\tau)\left(\log{n} + (q-1)\log{\frac{\pi}{2}}\right)} +\mathcal{O}\left(\frac{n}{\log{n}(q+\log{n})}\right)$ capable of correcting $\tau k$ errors at the channel output, where $0\le \tau < \frac{q-1}{2q}$. Furthermore, we present an explicit construction of signature codewords with polynomial complexity being able to correct up to $\left( \frac{q-1}{8q} - \epsilon\right)k$ errors for a codeword length $k = \mathcal{O} \left ( \frac{n}{\log \log n} \right )$, where $\epsilon$ is a small non-negative number. Moreover, we prove several non-existence results (converse bounds) for $q$-ary signature codes enabling error correction., Comment: 12 pages, 0 figures, submitted to 2022 IEEE Information Theory Workshop

Cryptographic algorithms rely on the secrecy of their corresponding keys. On embedded systems with standard CMOS chips, where secure permanent memory such as flash is not available as a key storage, the secret key can be derived from Physical Unclonable Functions (PUFs) that make use of minuscule manufacturing variations of, for instance, SRAM cells. Since PUFs are affected by environmental changes, the reliable reproduction of the PUF key requires error correction. For silicon PUFs with binary output, errors occur in the form of bitflips within the PUFs response. Modelling the channel as a Binary Symmetric Channel (BSC) with fixed crossover probability $p$ is only a first-order approximation of the real behavior of the PUF response. We propose a more realistic channel model, refered to as the Varying Binary Symmetric Channel (VBSC), which takes into account that the reliability of different PUF response bits may not be equal. We investigate its channel capacity for various scenarios which differ in the channel state information (CSI) present at encoder and decoder. We compare the capacity results for the VBSC for the different CSI cases with reference to the distribution of the bitflip probability according a work by Maes et al.