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

Abstract

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.

To be presented at the IEEE 2010 International Symposium on Information Theory

References in corpus (1)

• Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels