Multivariate Analytic Combinatorics for Cost Constrained Channels
Andreas Lenz, Stephen Melczer, Cyrus Rashtchian, Paul H. Siegel

TL;DR
This paper applies multivariate analytic combinatorics to analyze the asymptotic behavior of sequences in cost-constrained channels, linking graph structures to generating function singularities and generalizing channel capacity results.
Contribution
It introduces a novel approach connecting analytic combinatorics and graph theory to study cost-constrained channels, extending classical capacity results.
Findings
Derived asymptotic formulas for cost-limited sequence counts
Linked channel capacity to singularities of generating functions
Provided a new proof of capacity equivalence
Abstract
Analytic combinatorics in several variables is a branch of mathematics that deals with deriving the asymptotic behavior of combinatorial quantities by analyzing multivariate generating functions. We study information-theoretic questions about sequences in a discrete noiseless channel under cost constraints. Our main contributions involve the relationship between the graph structure of the channel and the singularities of the bivariate generating function whose coefficients are the number of sequences satisfying the constraints. We use these new results to invoke theorems from multivariate analytic combinatorics to obtain the asymptotic behavior of the number of cost-limited strings that are admissible by the channel. This builds a new bridge between analytic combinatorics in several variables and labeled weighted graphs, bringing a new perspective and a set of powerful results to the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsDNA and Biological Computing · Algorithms and Data Compression · Advanced biosensing and bioanalysis techniques
