Rank Modulated Composite Encoding for Data Storage in DNA

Tomer Cohen
Technion – Israel Institute of Technology

Abstract:

The talk focuses on the integration of composite DNA alphabets and
rank modulation, two promising paradigms for high-density DNA-based data storage. Composite DNA leverages the inherent
redundancy of synthesis by representing positions as mixtures of nucleotides, while rank modulation utilizes the
relative ordering of these motifs to provide robustness against signal variations. We first address this combination
through a framework of fixed-length permutations subject to ranking errors measured by Kendall’s tau distance. For
this setting, we establish the channel capacity and present a construction for sequences of ranked symbols using Tensor
Permutation Codes (TPC). We then extend the theory to a more physically faithful model involving variable-length
permutations, specifically addressing insertion and deletion (indel) errors occurring at the "tail" of the
ranking, the lower-frequency motifs. Within this paradigm, we establish a theoretical equivalence between tail deletion,
insertion, and indel codes, and provide optimal constructions for both individual symbols and sequences via Tail Tensor
Permutation Codes (TTPC). Together, these results offer a comprehensive theoretical and practical framework for
leveraging rank-modulated composite symbols in error-resilient DNA storage systems.

Biography:

Tomer Cohen is a Ph.D. candidate in the Faculty of Computer Science at the Technion –
Israel Institute of Technology. He earned a dual B.Sc. in Computer Science and Mathematics from the Technion. Tomer
began his graduate studies under the supervision of Prof. Eitan Yaakobi and is currently co-advised by Prof. Antonia
Wachter-Zeh in the direct Ph.D. Track. His research interests lie in information theory and coding theory, with a
primary focus on developing error-correction schemes for DNA-based data storage systems.