Exact Asymptotics for Discrete Noiseless Channels

Analytic combinatorics in several variables (ACSV) is a powerful tool for deriving the asymptotic behavior of combinatorial quantities by analyzing multivariate generating functions. We use ACSV to derive the first-order sub-exponential asymptotics of sequences generated by a discrete noiseless channel under an average cost constraint. As a by-product of the analysis, we obtain a new proof of the equivalence of the combinatorial and probabilistic definitions of the cost-constrained capacity.