Algebraic matching techniques for fast decoding of polar codes with Reed-Solomon kernel

TL;DR

This paper introduces an algebraic decoding approach that leverages Reed-Solomon code properties to enable faster, near-ML decoding of polar codes with Reed-Solomon kernels, reducing complexity.

Contribution

It presents a generalized order statistics algorithm for soft decoding of Reed-Solomon codes and applies it to polar codes with Reed-Solomon kernels, enhancing decoding efficiency.

Findings

Reduced decoding complexity for polar codes with Reed-Solomon kernels

Achieved near-ML decoding performance

Leveraged algebraic properties for improved reprocessing

Abstract

We propose to reduce the decoding complexity of polar codes with non-Arikan kernels by employing a (near) ML decoding algorithm for the codes generated by kernel rows. A generalization of the order statistics algorithm is presented for soft decoding of Reed-Solomon codes. Algebraic properties of the Reed-Solomon code are exploited to increase the reprocessing order. The obtained algorithm is used as a building block to obtain a decoder for polar codes with Reed-Solomon kernel.