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We derive upper and lower bounds on the reliability function for thecommon-message discrete memoryless broadcast channel with variable-lengthfeedback. We show that the bounds are tight when the broadcast channel isstochastically degraded. For the achievability part, we adapt Yamamoto andItoh's coding scheme by controlling the expectation of the maximum of a set ofstopping times. For the converse part, we adapt Burnashev's proof techniquesfor establishing the reliability functions for (point-to-point) discretememoryless channels with variable-length feedback and sequential hypothesistesting.

On the Reliability Function of the Common-Message Broadcast Channel with Variable-Length Feedback