Asymptotics Of The Random Coding Error Probability For Constant-Composition Codes

Saddlepoint approximations to the error probability are derived for multiple-cost-constrained random coding ensembles where codewords satisfy a set of constraints. Constant-composition inputs over a binary symmetric channel are studied as a particular case. For codewords with equiprobable empirical distribution, the analysis recovers the same error exponent and pre-exponential polynomial decay as the uniform i.i.d. ensemble and provides an explicit formula for the loss in prefactor (third-order term) incurred by the constant-composition ensemble.