Optimization-Theoretic Analysis of Nanopore Sequencing Channels

Nanopore sequencing produces variable-length, context-dependent observations affected by substitutions, insertions, deletions, and enzyme-driven dwell-time fluctuations. The resulting channel couples symbol uncertainty with synchronization variability and biophysical context. We develop an optimization-theoretic framework for context-dependent insertion-deletion-substitution (CIDS) models augmented with random dwell times. Capacity approximation, parameter estimation, decoding, and redundancy allocation are cast as structured optimization problems via variational mutual-information forms, saddle-point bounds, EM-type likelihood maximization with latent alignments, and constrained redundancy division. Synthetic experiments illustrate key behaviors and provide design guidance for nanopore-based DNA communication and storage systems.