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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.

Various Views on the Trapdoor Channel and an Upper Bound on its Capacity