A Wringing-Based Proof of a Second-Order Converse for the Multiple-Access Channel under Maximal Error Probability

The second-order converse bound of multiple access channels is an intriguing problem in information theory. In this work, in the setting of the two-user discrete memoryless multiple access channel (DM-MAC) under the maximal error probability criterion, we investigate the gap between the best achievable rates and the asymptotic capacity region. With “wringing techniques” and meta-converse arguments, we show that gap at blocklength $n$ is upper bounded by $O(1/\sqrt{n})$.