论文标题
通过扭动依赖性，多访问通道的二阶匡威结合
A Second-Order Converse Bound for the Multiple-Access Channel via Wringing Dependence
论文作者
论文摘要
在误差约束的平均概率下，为两用户多访问通道提供了新的匡威结合。该约束表明，对于大多数感兴趣的渠道，二阶编码速率（即最佳可实现率与渐近容量区域之间的差异是具有固定误差概率的块长度$ n $的函数 - 为$ o（1/\ sqrt {n}）$每个通道使用。这种相反的证明背后的主要工具是两个随机变量之间的依赖性的新量度，称为扭动依赖性，因为它是受Ahlswede的扭动技术的启发。 $ o（1/\ sqrt {n}）$差距显示出满足某些规律性条件的任何通道，其中包括所有离散的无障碍通道和高斯多个ACCESS通道。确切的上限是误差概率的函数，在$ O（1/\ sqrt {n}）$项中的系数证明了该系数，尽管对于大多数频道，它们与现有可实现的界限不匹配。
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.
