Equidistant Polarizing Transforms

This paper presents a non-binary polar coding scheme that can reach the equidistant distant spectrum bound for discrete memoryless channels. This is the best that can be reached up to now and is tight for additive white Gaussian channels. To do this, we first define the equidistant property for the polarizing transforms. We have designed transforms that have better distance characteristics using a simple procedure for signal sets. Furthermore, we designed a new four-component signal set in two dimensions to define the equidistant transform for q = 4. We follow Şaşoğlu’s work, which introduces polarizing transforms of all channels for any input alphabet size and defines some constraints to avoid a polarization anomaly. Alternatively, we removed the negative effect of the anomaly on polarization by using transforms with appropriate distance properties. Finally, the speed of polarization is significantly increased by using the proposed transforms with better distance characteristics. Moreover, we show improvement in error performance. Index Terms Channel polarization, equidistant channel, non-binary polar codes, phase shift keying, polarizing transform, signal set design.