  We consider non-binary polarization transform problem of polar codes. The
focus of this work is on finding equidistant (or almost equidistant) polarizing
transforms to maximize the minimum distance and to approach the equidistant
distant spectrum bound as a function of signal set. This bound is an ultimate
limit and tight for additive white Gaussian channels. In this way, polarization
of error probability for the good channel is improved while the bad channel is
almost the same for a given signal set. Our main result is that the
polarization speed is increased by using polarizing transform with an improved
distance profile. A non-binary polarization transform for q = 5 is found that
can provide the equidistant distant spectrum bound. Almost equidistant
polarization transforms for q = 4, 6, 7 and 8 are introduced for PSK signal
sets. As a private solution, we provided new geometries for the signal set
design to define the equidistant transform for q = 3 and q = 4 for one and two
dimensional signalings. We proposed a procedure to design transforms that have
better distance profiles for q-ary signal sets. Finally, we show improvements
in frame error rates.
