An entropy inequality for q-ary random variables and its application to channel polarization

It is shown that given two copies of a q-ary input channel W, where q is prime, it is possible to create two channels W⁻ and W⁺ whose symmetric capacities satisfy I(W⁻) ≤ I(W) ≤ I(W⁺), where the inequalities are strict except in trivial cases. This leads to a simple proof of channel polarization in the q-ary case.