Refined Strong Converse for the Constant Composition Codes

A strong converse bound for constant composition codes of the form $P_{\mathbf{e}}^{(n)} \geq 1 - A{n^{ - 0.5\left( {1 - E_{sc}^\prime (R,W,p)} \right)}}{e^{ - n{E_{sc}}(R,W,p)}}$ 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.