A Note on Parallel Asynchronous Channels with Arbitrary Skews

TL;DR

This paper determines the exact zero-error capacity of a parallel asynchronous communication channel with arbitrary skews, confirming the previously known achievable rate as optimal.

Contribution

It proves that the known zero-error coding scheme's rate is the maximum possible for the described channel.

Findings

Zero-error capacity equals the asymptotic rate log2(1+√5)-1.

The established capacity matches the previously known achievable rate.

The result confirms the optimality of the existing coding scheme.

Abstract

A zero-error coding scheme of asymptotic rate $ \log_2 (1+\sqrt{5}) - 1 $ was recently described for a communication channel composed of parallel asynchronous lines satisfying the so-called no switch assumption. We prove that this is in fact the highest rate attainable, i.e., the zero-error capacity of this channel.