On the Error Exponents for Common Message Broadcasting over DMCs with Feedback

We investigate the achievable probability of error in a communication setup where a single transmitter broadcasts an common message sequence to a set of receivers. The communication is aided by the availability of perfect causal feedback of all the received symbols to the encoder. Two types of schemes are considered: in the first model, the encoder and the decoders have to agree in advance on the sequence number of the intended message, whereas the decoders should also Figure out the sequence number from the received symbols in the second model. The former is called coordinated message transmission, and latter is named streaming block transmission. The challenge faced in both models is to appropriately synchronize the independent receivers, while leveraging the boost in error probability due to feedback. We propose error exponents, which are optimal for a class of broadcast channels under coordinated message transmission. We propose an achievable exponent under streaming block transmission. These results extend the best known single receiver results.