A new converse bound is presented for the two-user multiple-access channel under the average probability of error constraint. This bound shows that for most channels of interest, the second-order coding rate -- that is, the difference between the best achievable rates and the asymptotic capacity region as a function of blocklength $n$ with fixed probability of error -- is $O(1/\sqrt{n})$ bits per channel use. The principal tool behind this converse proof is a new measure of dependence between two random variables called wringing dependence, as it is inspired by Ahlswede's wringing technique. The $O(1/\sqrt{n})$ gap is shown to hold for any channel satisfying certain regularity conditions, which includes all discrete-memoryless channels and the Gaussian multiple-access channel. Exact upper bounds as a function of the probability of error are proved for the coefficient in the $O(1/\sqrt{n})$ term, although for most channels they do not match existing achievable bounds.

翻译：在平均误差概率限制下,为双用户多存通道提供了一个新的反向约束。 该约束显示,对于大多数感兴趣的频道来说,第二顺序编码率 -- -- 即最佳可实现率和无反应能力区域之间的差值,是块长美元(固定误差概率为美元)的函数,每个频道使用美元(1/\sqrt{n})美元。这一反向证据背后的主要工具是两个随机变量之间的依赖度的新度,这两个变量被称为皱纹依赖性,因为它受Ahlswede的转环技术的启发。 $O(1/\sqrt{n})$( $( 1/\sqrt{n}) 显示, 任何频道只要满足某些常规性条件, 包括所有不独立- 模拟通道和高斯多存通道, 就会存在一定的差额。 在 $O( 1/\\ sqrt{n} 术语中, 对系数的超值上限功能被证明, 尽管大多数频道都不符合现有可实现的界限。