Rate-Compatible Punctured Polar Codes: Optimal Construction Based on Polar Spectra

TL;DR

This paper introduces a systematic framework for designing rate-compatible punctured polar codes with arbitrary lengths using polar spectra, optimizing performance criteria, and outperforming turbo codes in LTE systems.

Contribution

It proposes a novel polar spectra-based method for optimal puncturing in polar codes, enabling arbitrary lengths and improved performance without exhaustive search.

Findings

Maximized spectrum distances lead to better code performance.

Proposed schemes outperform turbo codes in LTE simulations.

Universal puncturing tables are achieved without exhaustive search.

Abstract

Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the corresponding code length is limited to the power of two. In this paper, we establish a systematic framework to design the rate-compatible punctured polar (RCPP) codes with arbitrary code length. A new theoretic tool, called polar spectra, is proposed to count the number of paths on the code tree with the same number of zeros or ones respectively. Furthermore, a spectrum distance SD0 (SD1) and a joint spectrum distance (JSD) are presented as performance criteria to optimize the puncturing tables. For the capacity-zero puncturing mode (punctured bits are unknown to the decoder), we propose a quasi-uniform puncturing algorithm, analyze the number of equivalent puncturings and prove that this scheme can maximize SD1 and JSD. Similarly, for the capacity-one mode (punctured bits are known to the decoder), we also devise a reversal quasi-uniform puncturing scheme and prove that it has the maximum SD0 and JSD. Both schemes have a universal puncturing table without any exhausted search. These optimal RCPP codes outperform the performance of turbo codes in LTE wireless communication systems.