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A new single-letter achievable rate region is proposed for the two-user discrete memoryless Multiple-Access Channel(MAC) with noiseless feedback. The proposed region includes the Cover-Leung rate region, and it is shown that the inclusion is strict. The proof uses a block-Markov superposition strategy based on the observation that the messages of the two users are correlated given the feedback. The rates of transmission are too high for each encoder to decode the other's message directly using the feedback, so they transmit correlated information in the next block to learn the message of one another. They then cooperate in the following block to resolve the residual uncertainty of the decoder.
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