Window Processing of Binary Polarization Kernels

TL;DR

This paper introduces an improved window processing decoding algorithm for binary polarization kernels that reduces complexity and enhances performance of polar codes with larger kernels.

Contribution

It presents a lower-complexity, LLR-based window processing algorithm that reuses computations, improving decoding efficiency for larger polarization kernels of size 16 and 32.

Findings

Lower arithmetic complexity achieved

Enhanced polarization properties of kernels

Better performance and reduced decoding complexity

Abstract

A decoding algorithm for polar (sub)codes with binary $2^t\times 2^t$ polarization kernels is presented. It is based on the window processing (WP) method, which exploits the linear relationship of the polarization kernels and the Arikan matrix. This relationship enables one to compute the kernel input symbols probabilities by computing the probabilities of several paths in Arikan successive cancellation (SC) decoder. In this paper we propose an improved version of WP, which has significantly lower arithmetic complexity and operates in log-likelihood ratios (LLRs) domain. The algorithm identifies and reuses common subexpressions arising in computation of Arikan SC path scores. The proposed algorithm is applied to kernels of size 16 and 32 with improved polarization properties. It enables polar (sub)codes with the considered kernels to simultaneously provide better performance and lower decoding complexity compared with polar (sub)codes with Arikan kernel.