Random coding theorem for broadcast channels with degraded components

Absfroct-This paper generalizes Cover’s results on broadcast channels with two binary symmetr ic channels (BSC) to the class of degraded channels with N components. A random code, and its associated decoding scheme, is shown to have expected probability of error going to zero for all components simultaneously as the codeword length goes to infinity, if the point representing the rates to the various receivers falls in the set of achievable rates described by this paper. A procedure to expurgate a good random broadcast code is given, leading to a bound on the max imum probability of error. Binary symmetr ic broadcast channels always fall in the class of degraded broadcast channels. The results of the paper are applied to this class of channels of potential practical importance.