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

Channel Upgradation for Non-Binary Input Alphabets and MACs