Imagine an information source (a DMS *X*) with *X* = {0, 1}, *p*(*x*_{0}) =
0.4, *p*(*x*_{1}) = 0.6, *H*(*X*) = 0.97095 emitting symbol *x _{i}* into an information channel. Now assume that the information channel is broken down to two parts resulting in a 3-level output (

*Y*

^{3}) and a 2-level output (

*Y*

^{2}).

A directed graph can then be shown for the part of the information channel prior to the break down as

❶

Because the information channel gets broken down, this directed graph can be sliced between the confounding zones. Therefore, slicing of the outputs creates the Erasure Channel (e, erasure) and the Binary Symmetric Channel (BSC).

The directed graphs for the two parts of the information channel are therefore

❷

The mutual information for the respective channels are then

*I*(

*X*;

*Y*) of

*Y*

^{3}Erasure Channel >

*Y*

^{2}BSC

*Y*

^{3}Erasure Channel. ❸