论文标题
在删除通道的对称性上
On the Symmetries of the Deletion Channel
论文作者
论文摘要
在本文中，我们考虑了与通信渠道相关的一类对称组，这些对称组可以非正式地看作是通过频道的作用``通勤''的一组输入的转换。这些组首先是由Polyanskiy在（Ieeetoit 2013）中研究的。我们表明了一个简单的结果，即获得给定信道的最大互相信息的输入分布是其组的``固定点''。我们猜想（并提供经验证据），缺失通道的通道组极小（其中包含许多元素在区块长度中常数）。我们证明了这种猜想的特殊情况。这是为什么对二进制删除渠道的分析比其无记忆的同行更加困难的原因。
In this paper, we consider a class of symmetry groups associated to communication channels, which can informally be viewed as the transformations of the set of inputs that ``commute'' with the action of the channel. These groups were first studied by Polyanskiy in (IEEEToIT 2013). We show the simple result that the input distribution that attains the maximum mutual information for a given channel is a ``fixed point'' of its group. We conjecture (and give empirical evidence) that the channel group of the deletion channel is extremely small (it contains a number of elements constant in the blocklength). We prove a special case of this conjecture. This serves as some formal justification for why the analysis of the binary deletion channel has proved much more difficult than its memoryless counterparts.
