Performance Limits and Practical Decoding of Interleaved Reed-Solomon Polar Concatenated Codes

TL;DR

This paper introduces a concatenated coding scheme combining polar codes with interleaved Reed-Solomon codes, achieving capacity with improved error decay and practical decoding algorithms for finite block lengths.

Contribution

It demonstrates that concatenating polar codes with Reed-Solomon codes retains capacity-achieving properties and enhances error decay rates, along with proposing efficient decoding algorithms.

Findings

Capacity-achieving with error probability less than 2^{-N^{1-psilon}}

Improved error decay rate over standard polar codes

Effective decoding algorithms for finite block lengths

Abstract

A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon 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 $2^{-N^{0.5-\epsilon}}$, the frame error probability of Arikan's polar codes. The proposed concatenated polar codes and Arikan's polar codes are also compared for transmission over channels with erasure bursts. We provide a sufficient condition on the length of erasure burst which guarantees failure of the polar decoder. On the other hand, it is shown that the parameters of the concatenated polar code can be set in such a way that the capacity-achieving properties of polar codes are preserved. 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.