A partial ordering for binary channels

The properties of iterated binary channels are investigated. An ordering (defined by the symbol
\supset
) of communication channels with two possible inputs and any number of possible outputs is defined. For any two such channels
C_1
and
C_2
, this ordering has the property that if
C_1 \supset C_2
, the minimum average loss when using
C_1
will be less than the minimum average loss using
C_2
, independent of the losses assigned to the various errors, and independent of the statistics of the source. This ordering is applied to 1) the general binary channel, 2) the iterated binary symmetric channel, and 3) the unreliable binary symmetric channel when used with many iterations. Curves allowing one to use the ordering are given, and an example using these curves is worked out.