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In this work, a new upper bound for average error probability of a two-user Discrete Memoryless (DM) Multiple-Access Channel (MAC) is derived. This bound can be universally obtained for all discrete memoryless MACs with given input and output alphabets. This is the first bound of this type that explicitly uses the method of the expurgation. It is shown that the exponent of this bound is greater than or equal to those of previously known bounds.
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