Refined Strong Converse for the Constant Composition Codes

A strong converse bound for constant composition codes of the form $P_e^{(n)}\ge 1-A{n}^{-0.5(1-E_{sc}^{\mathrm{\prime }}(R,W,p))}{e}^{-n{E}_{sc}(R,W,p)}$ is established using the Berry-Esseen theorem through the concepts of Augustin information and Augustin mean, where $A$ is a constant determined by the channel $W$, the composition $p$, and the rate $R$, i.e., $A$ does not depend on the block length $n$.