Interlocked permutations

TL;DR

This paper investigates the zero-error capacity of channels with infinite input alphabets, providing combinatorial solutions for three specific channels and extending permutation capacity theory.

Contribution

It offers new combinatorial solutions to the zero-error capacity problem for certain infinite-alphabet channels, expanding the understanding of permutation capacity.

Findings

Solved the zero-error capacity for three specific channels

Extended permutation capacity theory to infinite alphabets

Provided combinatorial methods for capacity analysis

Abstract

The zero-error capacity of channels with a countably infinite input alphabet formally generalises Shannon's classical problem about the capacity of discrete memoryless channels. We solve the problem for three particular channels. Our results are purely combinatorial and in line with previous work of the third author about permutation capacity.