An outer bound for E-capacity region of broadcast channel giving a new outer bound for capacity region

The discrete memoryless broadcast channel without a common message is considered. The outer bound of the E-capacity region in the case of average error probability is constructed. When E→0 we obtain an outer bound for the capacity region. For the deterministic channels this bound coincides with the capacity region found independently by Pinsker (1978) and Marton (1979)