Capacity Problem of Trapdoor Channel

Abstract

The capacity problem of the trapdoor channel is one of famous long-standing problems. The trapdoor channel considered by Blackwell [1] is a typical example of channel with memory. Ash [2] expressed the channel by using two channel matrices with four states, while the expression does not necessarily make the problem tractable. We provided an interesting recurrence giving the explicit expression of the conditional distributions of the channel output sequences given input sequences of length n [5]. In order to determine the capacity of this special channel, we have to understand the fractal structure buried in the channel matrices between input and output sequences of long length.