Efficient Belief Propagation List Ordered Statistics Decoding of Polar Codes

TL;DR

This paper introduces efficient decoding algorithms for polar codes over BEC and AWGNC, combining maximum likelihood, belief propagation list, and ordered statistics decoding to improve performance and reduce complexity.

Contribution

It presents a novel exact ML decoding algorithm for BEC and an enhanced decoding scheme for AWGNC combining CBPL and OSD, with efficient implementation and parallelization strategies.

Findings

The BEC decoding algorithm achieves exact ML decoding with manageable complexity.

The combined CBPL and OSD approach significantly outperforms plain CBPL.

Parallel implementation reduces decoding latency.

Abstract

New algorithms for efficient decoding of polar codes (which may be CRC-augmented), transmitted over either a binary erasure channel (BEC) or an additive white Gaussian noise channel (AWGNC), are presented. We start by presenting a new efficient exact maximum likelihood decoding algorithm for the BEC based on inactivation decoding and analyze its computational complexity. This algorithm applies a matrix triangulation process on a sparse polar code parity check matrix, followed by solving a small size linear system over GF(2). We then consider efficient decoding of polar codes, transmitted over the AWGNC. The algorithm applies CRC-aided belief propagation list (CBPL) decoding, followed by ordered statistics decoding (OSD) of low order. Even when the reprocessing order of the OSD is as low as one, the new decoder is shown to significantly improve on plain CBPL. To implement the OSD efficiently, we adapt the matrix triangulation algorithm from the BEC case. We also indicate how the decoding algorithms can be implemented in parallel for low latency decoding. Numerical simulations are used to evaluate the performance and computational complexity of the new algorithms.