Constructing an LDPC Code Containing a Given Vector

The coding problem considered in this work is to construct a linear code $\mathcal{C}$ of given length $n$ and dimension $k<n$ such that a given binary vector $\mathbf{r} \in \mathbb{F}^{n}$ is contained in the code. We study a recent solution of this problem by M\"uelich and Bossert, which is based on LDPC codes. We address two open questions of this construction. First, we show that under certain assumptions, this code construction is possible with high probability if $\mathbf{r}$ is chosen uniformly at random. Second, we calculate the uncertainty of $\mathbf{r}$ given the constructed code $\mathcal{C}$. We present an application of this problem in the field of Physical Unclonable Functions (PUFs).Comment: 5 pages, accepted at the International Workshop on Algebraic and Combinatorial Coding Theory, 201

On the Key Generation Rate of Physically Unclonable Functions

In this paper, an algebraic binning based coding scheme and its associated achievable rate for key generation using physically unclonable functions (PUFs) is determined. This achievable rate is shown to be optimal under the generated-secret (GS) model for PUFs. Furthermore, a polar code based polynomial-time encoding and decoding scheme that achieves this rate is also presented