Gökberk Erdoğan | Searcharxiv

arXiv2026

Private Information Retrieval for Large-Scale DNA-Based Data Storage

We investigate Private Information Retrieval (PIR) in the context of synthetic DNA-based data storage. While PIR is a well-studied primitive for digital databases, extending it to DNA-based databases presents unique challenges arising from biochemical query mechanisms and their complexity. We propose two approaches for adapting two-server PIR protocols to DNA-based storage, balancing privacy, efficiency, and feasibility. These approaches illustrate how information-theoretic privacy trade-offs manifest in DNA-based storage systems.

cs.IR↗

arXiv2022

Signature Codes for a Noisy Adder Multiple Access Channel

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 $k = \frac{2n\log{3}}{(1-2τ)\left(\log{n} + (q-1)\log{\fracπ{2}}\right)} +\mathcal{O}\left(\frac{n}{\log{n}(q+\log{n})}\right)$ capable of correcting $τk$ errors at the channel output, where $0\le τ< \frac{q-1}{2q}$. Furthermore, we present an explicit construction of signature codewords with polynomial complexity being able to correct up to $\left( \frac{q-1}{8q} - ε\right)k$ errors for a codeword length $k = \mathcal{O} \left ( \frac{n}{\log \log n} \right )$, where $ε$ is a small non-negative number. Moreover, we prove several non-existence results (converse bounds) for $q$-ary signature codes enabling error correction.

cs.IT↗