  Consider a single-user or multiple-access channel with a large output
alphabet. A method to approximate the channel by an upgraded version having a
smaller output alphabet is presented and analyzed. The original channel is not
necessarily symmetric and does not necessarily have a binary input alphabet.
Also, the input distribution is not necessarily uniform. The approximation
method is instrumental when constructing capacity achieving polar codes for an
asymmetric channel with a non-binary input alphabet. Other settings in which
the method is instrumental are the wiretap setting as well as the lossy source
coding setting.
