arXiv subjects

Franziska Weindel

Publications and source records attributed to Franziska Weindel.

4 recordsLinked to original sources

arXiv2026

LLM-Guided Search for Deletion-Correcting Codes

Finding deletion-correcting codes of maximum size has been an open problem for over 70 years, even for a single deletion. We adapt FunSearch, a large language model (LLM)-guided evolutionary search, to discover functions that construct deletion-correcting codes at short code lengths. For a single deletion, our search finds a function that we prove constructs the conjectured-optimal Varshamov-Tenengolts code. For multiple deletions and quaternary edit codes, the discovered functions improve on prior explicit, search-based, and neural constructions but remain empirical heuristics without new theoretical insights. We study design choices for LLM-guided evolutionary search and find that, for our problem, compute is better allocated to sampling more functions than to longer reasoning traces per function, and that co-evolving natural language descriptions with code hurts search quality. We propose deduplicating logically identical functions during evolution, which we find critical for search diversity. Our results demonstrate the potential of LLM-guided evolutionary search for information theory and code design and represent the first application of such methods for constructing error-correcting codes. However, in our current formulation, evaluating a function scales exponentially with code length, limiting the approach to short codes.

cs.AI↗

arXiv2026

Trace Reconstruction with Language Models

The general trace reconstruction problem seeks to recover an original sequence from its noisy copies independently corrupted by insertions, deletions, and substitutions. This problem arises in applications such as DNA data storage, a promising storage medium due to its high information density and longevity. However, errors introduced during DNA synthesis, storage, and sequencing require correction through algorithms and codes, with trace reconstruction often used as part of data retrieval. In this work, we propose TReconLM, a decoder-only transformer that solves trace reconstruction as a next-token prediction task. TReconLM outperforms state-of-the-art trace reconstruction algorithms, including prior deep-learning approaches, recovering a substantially higher fraction of sequences without error. We pretrain on synthetic data generated from a simple error model and fine-tune on real-world data to adapt to technology-specific error patterns. Code is available at https://github.com/MLI-lab/TReconLM.

cs.LG↗

arXiv2025

Transformer-Based Decoding in Concatenated Coding Schemes Under Synchronization Errors

We consider the reconstruction of a codeword from multiple noisy copies that are independently corrupted by insertions, deletions, and substitutions. This problem arises, for example, in DNA data storage. A common code construction uses a concatenated coding scheme that combines an outer linear block code with an inner code, which can be either a nonlinear marker code or a convolutional code. Outer decoding is done with Belief Propagation, and inner decoding is done with the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. However, the BCJR algorithm scales exponentially with the number of noisy copies, which makes it infeasible to reconstruct a codeword from more than about four copies. In this work, we introduce BCJRFormer, a transformer-based neural inner decoder. BCJRFormer achieves error rates comparable to the BCJR algorithm for binary and quaternary single-message transmissions of marker codes. Importantly, BCJRFormer scales quadratically with the number of noisy copies. This property makes BCJRFormer well-suited for DNA data storage, where multiple reads of the same DNA strand occur. To lower error rates, we replace the Belief Propagation outer decoder with a transformer-based decoder. Together, these modifications yield an efficient and performant end-to-end transformer-based pipeline for decoding multiple noisy copies affected by insertion, deletion, and substitution errors. Additionally, we propose a novel cross-attending transformer architecture called ConvBCJRFormer. This architecture extends BCJRFormer to decode transmissions of convolutional codewords, serving as an initial step toward joint inner and outer decoding for more general linear code classes.

cs.IT↗

arXiv2024

Embracing Errors Is More Efficient Than Avoiding Them Through Constrained Coding for DNA Data Storage

DNA is an attractive medium for digital data storage. When data is stored on DNA, errors occur, which makes error-correcting coding techniques critical for reliable DNA data storage. To reduce the errors, a common technique is to include constraints that avoid homopolymers (consecutive repeated nucleotides) and balance the GC content, as sequences with homopolymers and unbalanced GC content are often associated with higher error rates. However, constrained coding comes at the cost of an increase in redundancy. An alternative is to control errors by randomizing the sequences, embracing errors, and paying for them with additional coding redundancy. In this paper, we determine the error regimes in which embracing substitutions is more efficient than constrained coding for DNA data storage. Our results suggest that constrained coding for substitution errors is inefficient for existing DNA data storage systems. Theoretical analysis indicates that for constrained coding to be efficient, the increase in substitution errors for nucleotides in homopolymers and sequences with unbalanced GC content must be very large. Additionally, empirical results show that the increase in substitution, deletion, and insertion rates for these nucleotides is minimal in existing DNA storage systems.

cs.IT↗