Universal channel coding with continuous output system

We propose a universal channel coding for continuous output system with a parametric family of channels. Our encoder is the same as the previous paper [CMP 289, 1087]. For our decoding process, we invent α-Rényi divergence version of Clarke and Barron's formula for Bayesian average distribution, which are not required in the previous paper [CMP 289, 1087]. Combing this formula and the information spectrum method, we propose our universal decoder. We also derive a lower bound for the error exponent.