  This paper investigates the problem of information transmission over the
simultaneous relay channel with two users (or two possible channel outcomes)
where for one of them the more suitable strategy is Decode-and-Forward (DF)
while for the other one is Compress-and-Forward (CF). In this setting, it is
assumed that the source wishes to send common and private informations to each
of the users (or channel outcomes). This problem is relevant to: (i) the
transmission of information over the broadcast relay channel (BRC) with
different relaying strategies and (ii) the transmission of information over the
conventional relay channel where the source is oblivious to the coding strategy
of relay. A novel coding that integrates simultaneously DF and CF schemes is
proposed and an inner bound on the capacity region is derived for the case of
general memoryless BRCs. As special case, the Gaussian BRC is studied where it
is shown that by means of the suggested broadcast coding the common rate can be
improved compared to existing strategies. Applications of these results arise
in broadcast scenarios with relays or in wireless scenarios where the source
does not know whether the relay is collocated with the source or with the
destination.
