A Simple Derivation of the Refined SPB for the Constant Composition Codes

A judicious application of the Berry-Esseen theorem via the concepts of Augustin information and mean is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is $\mathit{\Omega}\left(n^{-0.5(1-E_{sp}'(R,W,p))}\right)$ for the constant composition codes. The resulting non-asymptotic bounds have definite approximation error terms.