Evaluation of the Gilbert-Varshamov Bound using Multivariate Analytic Combinatorics

TL;DR

This paper applies multivariate analytic combinatorics to evaluate the Gilbert-Varshamov bound specifically for the sticky insertion and constrained-synthesis channels, providing precise asymptotic estimates.

Contribution

It introduces a novel application of analytic combinatorics in several variables to evaluate bounds in coding theory for specific channels.

Findings

Derived asymptotic estimates for the GV bound in new channel models

Extended analytic combinatorics methods to complex combinatorial quantities

Provided insights into the limits of coding for constrained channels

Abstract

Analytic combinatorics in several variables refers to a suite of tools that provide sharp asymptotic estimates for certain combinatorial quantities. In this paper, we apply these tools to determine the Gilbert-Varshamov (GV) bound for the sticky insertion and the constrained-synthesis channel.