Random-Coding Bounds for Some Broadcast Channels

The author establishes upper bounds for random coding for the decoding error probabilities in a discreet memoryless broadcast channel with two receivers, for the case of transmission of common and only private information. The bounds are more precise than those given in [B. D. Kudryashov and G. Sh. Poltyrev, Probl. Peredachi Inf., 1979, vol. 15, no. 3, pp. 3–17].