On the Construction and Decoding of Concatenated Polar Codes

TL;DR

This paper introduces a concatenated polar coding scheme with interleaved Reed-Solomon codes that achieves capacity and offers improved error decay rates and decoding performance at finite lengths.

Contribution

It presents a novel concatenation of polar and Reed-Solomon codes that enhances error decay and decoding efficiency while maintaining capacity achievement.

Findings

Achieves frame error probability less than 2^{-N^{1-ε}}

Improves error decay rate over original polar codes

Provides decoding algorithms with better finite-length performance

Abstract

A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any $\epsilon > 0$, and total frame length $N$, the parameters of the scheme can be set such that the frame error probability is less than $2^{-N^{1-\epsilon}}$, while the scheme is still capacity achieving. This improves upon $2^{-N^{0.5-\eps}}$, the frame error probability of Arikan's polar codes. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity.