Two novel views are presented on the trapdoor channel. First, by deriving theunderlying iterated function system (IFS), it is shown that the trapdoorchannel with input blocks of length $n$ can be regarded as the $n$th element ofa sequence of shapes approximating a fractal. Second, an algorithm is presentedthat fully characterizes the trapdoor channel and resembles the recursion ofgenerating all permutations of a given string. Subsequently, the problem ofmaximizing a $n$-letter mutual information is considered. It is shown that$\frac{1}{2}\log_2\left(\frac{5}{2}\right)\approx 0.6610$ bits per use is anupper bound on the capacity of the trapdoor channel. This upper bound, which isthe tightest upper bound known proves that feedback increases capacity of thetrapdoor channel.
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机译：活板通道上呈现了两种新颖的观点。首先，通过推导底层的迭代功能系统（IFS），表明具有长度为$ n $的输入块的陷门通道可以视为近似于分形的形状序列中的第$ n $个元素。其次，提出了一种算法，该算法可以完全表征陷门通道，并且类似于生成给定字符串的所有排列的递归。随后，考虑使$ n $个字母的互信息最大化的问题。结果表明，每次使用$ \ frac {1} {2} \ log_2 \ left（\ frac {5} {2} \ right）\约0.6610 $位是活板通道容量的上限。该上限是已知的最严格的上限，这证明了反馈会增加活板通道的容量。
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