  Let $X$ be a separated scheme of finite type over $k$ with $k$ being a
perfect field of positive characteristic $p$. In this work we define a complex
$K_{n,X,log}$ via Grothendieck's duality theory of coherent sheaves following
Kato and build up a quasi-isomorphism from the Kato-Moser complex of
logarithmic de Rham-Witt sheaves $\tilde \nu_{n,X}$ to $K_{n,X,log}$ for the
\'etale topology, and also for the Zariski topology under the extra assumption
$k=\bar k$. Combined with Zhong's quasi-isomorphism from Bloch's cycle complex
$\mathbb Z^c_{X}$ to $\tilde \nu_{n,X}$, we deduce certain vanishing, \'etale
descent properties as well as invariance under rational resolutions for higher
Chow groups of $0$-cycles with $\mathbb Z/p^n$-coefficients.
