# Multivariate Analytic Combinatorics for Cost Constrained Channels and Subsequence Enumeration

@article{Lenz2021MultivariateAC, title={Multivariate Analytic Combinatorics for Cost Constrained Channels and Subsequence Enumeration}, author={Andreas Lenz and Stephen Melczer and Cyrus Rashtchian and Paul H. Siegel}, journal={ArXiv}, year={2021}, volume={abs/2111.06105} }

Analytic combinatorics in several variables is a powerful tool for 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 and forbidden substring 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…

## One Citation

### Rate-Constrained Shaping Codes for Finite-State Channels With Cost

- Computer Science2022 IEEE International Symposium on Information Theory (ISIT)
- 2022

An equivalence is established between codes minimizing average symbol cost and codes minimizing total cost, and a separation theorem is proved, showing that optimal shaping can be achieved by a concatenation of optimal compression and optimal shaping for a uniform i.i.d. sources.

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