Channel dispersion for well-ordered mixed channels decomposed into memoryless channels

For a class of mixed channels that are decomposed into finitely many stationary memoryless channels, the optimum second-order coding rate, or equivalently, channel dispersion, is derived. The addressed channel, which is an instance of non-ergodic channels, is a sub-class of regular decomposable channels introduced by Winkelbauer. The second-order coding theorem can be viewed as an extension of the coding theorem established by Polyanskiy, Poor, and Verdú for the mixed channel of finitely many binary symmetric channels.