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 $I(W^-)\le I(W)\le I(W^+)$, where the inequalities are strict except in trivial cases. This leads to a simple proof of channel polarization in the q-ary case.

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