Bounds on $E$-Capacity of a Channel with a Random Parameter

We obtain a random-coding lower bound for the $E$-capacity of a channel with a random parameter under complete information about the encoder states [S. I. Gelfand and M. S. Pinsker, Probl. Contr. Inf. Theory, 9, no. 1, 19–31 (1980)] and also improve the upper bound of [E. A. Haroutunian and M. E. Haroutunian, Probl. Contr. Inf. Theory, 17, No. 2, 99–105 (1988)].