Error exponent of the common-message broadcast channel with variable-length feedback

We derive upper and lower bounds on the reliability function for the discrete memoryless broadcast channel with common message and variable-length feedback. We show that the bounds are tight when the broadcast channel is stochastically degraded. We adapt and supplement new ideas to Yamamoto and Itoh's two-phase coding scheme for the direct part and Burnashev's proof technique for the converse part.