Improving bounds on the capacity of the abstract nanopore channel

Derive sharper upper and lower bounds on the capacity C_f of the abstract nanopore channel across all mappings f: {A,C,G,T}^k -> {0,1,...,b-1}, for general window size k and number of current levels b, improving upon the current bounds (max_f C_f = min(log b, 2), min_f C_f ≥ (log b)/k, and min_f C_f ≤ 1 when b ≤ 2^k).

Background

The authors establish general bounds for the capacity C_f as a function of the pore size k and number of output levels b, and present exact computations for k=2 using their exponential-time algorithm. Their empirical results suggest possible nontrivial behavior (e.g., “bumpiness” in worst-case capacity) and that random balanced mappings tend to be closer to best-case than worst-case.

They explicitly state in the conclusion that much remains open and ask whether one can derive better bounds on the capacity, motivating tighter characterization of C_f across mappings f and parameters k and b.