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.