Behavior of Cascaded Binary Symmetric Channel for different number of cascades

A Binary Symmetric Channel is a communication model that transmits bits of information through the channel. The transmission is governed by the error probability of the channel. Network routes require multiple links which can be realized using cascaded channels. A single equivalent channel for a series of the identical cascaded binary symmetric channel is presented. The equivalent channel is analyzed for behavior with varying error probability of the individual building block channel. The difference in the behavior of the network for odd and even number of channels is considered. Information measures such as entropy, channel capacity, and mutual information are analyzed for a varying error probability and several cascades. The apparent response is explained through by the divergence of the error probability of the equivalent channel from the single individual channel. The previous works on cascaded Binary Symmetric Channels analyze the channel capacity in a cascaded setting of channels. This paper aims at monitoring the varying error probability primarily and inspecting the information measures with a change in error probability as well as the number of cascaded channels. The analyses help in determining the efficient operating area for a given number of cascades and error probability of the channel.