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In this paper we apply the "potential function method" introduced by the authors in (GA_SM) and (GA_CM) to prove a new outer bound on the capacity region of the deterministic-code arbitrarily varying general broadcast channel. Specializing by removing the variability of the channel, our outer bound gives another proof of the recent result of Liang, Kramer and Shamai, which is the currently best upper bound on the capacity region of the traditional broadcast channel (Liang-Kramer-Shamai).

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