  Let $k$ be a perfect field of positive characteristic and let $X$ be a smooth
irreducible quasi-compact scheme over $k$. The Drinfeld-Kedlaya theorem states
that for an irreducible $F$-isocrystal on $X$, the gap between consecutive
generic slopes is bounded by one. In this note we provide a new proof of this
theorem. Our proof utilizes the theory of $F$-isocrystals with $r$-log decay.
We first show that a rank one $F$-isocrystal with $r$-log decay is
overconvergent if $r<1$. Next, we establish a connection between slope gaps and
the rate of log-decay of the slope filtration. The Drinfeld-Kedlaya theorem
then follows from a simple patching argument.
