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

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.