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We investigate the maximum coding rate achievable over a two-user broadcastchannel for the scenario where a common message is transmitted usingvariable-length stop-feedback codes. Specifically, upon decoding the commonmessage, each decoder sends a stop signal to the encoder, which transmitscontinuously until it receives both stop signals. For the point-to-point case,Polyanskiy, Poor, and Verd\'u (2011) recently demonstrated that variable-lengthcoding combined with stop feedback significantly increases the speed at whichthe maximum coding rate converges to capacity. This speed-up manifests itselfin the absence of a square-root penalty in the asymptotic expansion of themaximum coding rate for large blocklengths, a result a.k.a. zero dispersion. Inthis paper, we show that this speed-up does not necessarily occur for thebroadcast channel with common message. Specifically, there exist scenarios forwhich variable-length stop-feedback codes yield a positive dispersion.

Broadcasting a Common Message with Variable-Length Stop-Feedback Codes