Theoretical and Practical Bounds on the Initial Value of Skew-Compensated Clock for Clock Skew Compensation Algorithm Immune to Floating-Point Precision Loss

TL;DR

This paper provides theoretical and practical bounds on the initial clock value for a skew compensation algorithm that is robust to floating-point precision issues, enhancing its reliability in digital communication systems.

Contribution

It offers the first systematic analysis of initial value bounds for a clock skew compensation algorithm, improving understanding of its initial conditions.

Findings

Derived theoretical bounds on initial clock values.

Validated bounds through practical analysis of floating-point errors.

Enhanced robustness of clock skew compensation algorithms.

Abstract

A clock skew compensation algorithm was recently proposed based on the extension of Bresenham's line drawing algorithm (Kim and Kang, IEEE Commun. Lett., vol. 26, no. 4, pp. 902--906, Apr. 2022), which takes into account the discrete nature of clocks in digital communication systems and mitigates the effect of limited floating-point precision on clock skew compensation. It lacks, however, a theoretical analysis of the range of the initial value of skew-compensated clock, which is also an initial condition for the proposed algorithm. In this letter, we provide practical as well as theoretical bounds on the initial value of skew-compensated clock based on a systematic analysis of the errors of floating-point operations, which replace the approximate bounds in Theorem 1 of the prior work.