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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&#x2212; and W+ whose symmetric capacities satisfy I(W&#x2212;) &#x2264; I(W) &#x2264; 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.

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