Improved Construction for Multiplicative Repetition Based Non-Binary Polar Codes

Conventional construction of non-binary polar codes divides the synthesized channels into the frozen channels and information channels. Each information channel carries one symbol i.e. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> bits. However, there are many middle channels with insufficient polarization, which can not carry one symbol of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> bits but only <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$i$</tex> bits, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 \leq i&lt;q, i \in \mathbb{Z}$</tex>, at finite block lengths. In this paper, we consider the bit-level construction for multiplicative repetition (MR) based non-binary polar codes and propose bitlevel improved construction for channel degradation method and Monte-Carlo method. Simulation results show that the proposed construction can significantly improve the decoding performance compared with the conventional construction scheme.