Timing Channel: Achievable Rate in the Finite Block-Length Regime

TL;DR

This paper analyzes the finite block-length capacity of the exponential server timing channel, providing a lower bound on achievable rates considering practical constraints and error probabilities.

Contribution

It introduces a Markov chain-based lower bound on the maximum coding rate for finite block-lengths in the exponential server timing channel.

Findings

Derived a lower bound on achievable rate as C - n^{-1/2} σ Q^{-1}(ε)

Provided a closed-form expression for the asymptotic variance σ^2

Quantified the impact of block-length and error probability on capacity

Abstract

The exponential server timing channel is known to be the simplest, and in some sense canonical, queuing timing channel. The capacity of this infinite-memory channel is known. Here, we discuss practical finite-length restrictions on the codewords and attempt to understand the maximal rate that can be achieved for a target error probability. By using Markov chain analysis, we prove a lower bound on the maximal channel coding rate achievable at blocklength $n$ and error probability $\epsilon$. The bound is approximated by $C- n^{-1/2} \sigma Q^{-1}(\epsilon)$ where $Q$ denotes the Q-function and $\sigma^2$ is the asymptotic variance of the underlying Markov chain. A closed form expression for $\sigma^2$ is given.