Polar Codes for Q-Ary Channels, <formula formulatype="inline"> <tex Notation="TeX">$q=2^{r}$</tex></formula>

We study polarization for nonbinary channels with input alphabet of size <i>q</i>=2<sup>r</sup>, <i>r</i>=2,3,.... Using Arıkan's polarizing kernel <i>H</i><sub>2</sub>, we prove that the virtual channels that arise in the process of channel evolution converge to <i>q</i>-ary channels with capacity 0,1,2,..., <i>r</i> bits. As a result of this analysis, we… CONTINUE READING