Sparsely Pre-transformed Polar Codes for Low-Latency SCL Decoding

TL;DR

This paper introduces a novel pre-transform technique for polar codes that improves low-latency SCL decoding performance by targeting specific error event sets, outperforming existing methods in practical scenarios.

Contribution

The paper proposes a new pre-transform method that enhances polar code decoding with small list sizes, addressing limitations of previous multi-layered transforms.

Findings

Outperforms state-of-the-art pre-transformed polar codes with small list sizes

Consistently improves decoding performance across various block lengths and code rates

Demonstrates effectiveness through extensive simulations

Abstract

Deep polar codes, employing multi-layered polar kernel pre-transforms in series, are recently introduced variants of pre-transformed polar codes. These codes have demonstrated the ability to reduce the number of minimum weight codewords, thereby closely achieving finite-block length capacity with successive cancellation list (SCL) decoders in certain scenarios. However, when the list size of the SCL decoder is small, which is crucial for low-latency communication applications, the reduction in the number of minimum weight codewords does not necessarily improve decoding performance. To address this limitation, we propose an alternative pre-transform technique to enhance the suitability of polar codes for SCL decoders with practical list sizes. Leveraging the fact that the SCL decoding error event set can be decomposed into two exclusive error event sets, our approach applies two different types of pre-transformations, each targeting the reduction of one of the two error event sets. Extensive simulation results under various block lengths and code rates have demonstrated that our codes consistently outperform all existing state-of-the-art pre-transformed polar codes, including CRC-aided polar codes and polarization-adjusted convolutional codes, when decoded using SCL decoders with small list sizes.