Rank Modulated Composite Encoding for Data Storage in DNA

Talk by Tomer Cohen

Date: 04.03.26  Time: 16.30 - 17.30  Room: Y27H28

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.