Upper bound to error probability for coding on bidirectional broadcast channels

The bidirectional broadcast channel denotes a broadcast channel with two receivers where each receiver knows the message intended for the other. Exponentially decreasing upper bounds on the average error probability using maximum likelihood decoders are derived based on Gallager´s results for the point-to-point channel. The bounds are coupled by the common input distribution and provide an alternative coding theorem using the random coding argument. Then the results are extended to include an average input constraint and to continuous-valued channels. For illustration the bidirectional broadcast channel with binary symmetric channels and with Gaussian channels and an average input power constraint are discussed in detail.