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Several existing resource allocation algorithms for broadcast OFDM channels require separate codewords for each user in each carrier. In channels with short blocks of constant fading values codewords that strech across several carriers are desirable. Thus, we propose an algorithm with low complexity where user-wise coding is possible by avoiding irresolvable decoding dependencies. We show by means of computer simulations that this algorithm outperforms a pure scheduling approach and still exploits significant amounts of the broadcast gain.