A New Inequality Related to Proofs of Strong Converse Theorems for Source or Channel Networks

In this paper we provide a new inequality useful for the proofs of strong converse theorems in the multiterminal information theory. We apply this inequality to the recent work by Tyagi and Watanabe on the strong converse theorem for the Wyner-Ziv source coding problem to obtain a new strong converse outer bound. This outer bound deviates from the Wyner-Ziv rate distortion region with the order $O\left(\frac{1}{\sqrt{n}}\right)$ on the length $n$ of source outputs.