Selectively Precoded Polar Codes

TL;DR

This paper introduces selectively precoded polar (SPP) codes, enhancing polar code performance with improved distance properties and near-capacity performance at short blocklengths, demonstrated through simulation results.

Contribution

The paper proposes a novel SPP code construction with encoding and decoding schemes, achieving near-capacity performance and better distance properties than existing polar code variants.

Findings

(128, 64) SPP code is 0.23 dB from the capacity limit at FER of 10^{-5}

SPP codes have superior distance properties compared to other polar code variants

Simulation results validate the effectiveness of the proposed SPP codes.

Abstract

In this paper, we propose \textit{selectively precoded polar (SPP) code}, built on top of Arikan's capacity achieving polar codes. We provide the encoding and decoding scheme for SPP code. Simulation results show that for a target frame erasure rate (FER) of $\mathbf{10^{-5}}$, a (128, 64) SPP code is just 0.23 dB away from the information theoretic limit at this blocklength. Further, it is also shown that such codes possess better distance properties compared to other contemporary polar code variants.