Efficient Maximum Likelihood Decoding of Polar Codes Over the Binary Erasure Channel

TL;DR

This paper introduces a novel efficient maximum likelihood decoding algorithm for polar codes over the binary erasure channel, utilizing matrix triangulation and belief propagation, with demonstrated low complexity and potential for parallel implementation.

Contribution

The paper presents a new decoding algorithm that combines matrix triangulation and belief propagation for polar codes over the binary erasure channel, improving efficiency.

Findings

The algorithm achieves exact maximum likelihood decoding.

It has lower computational complexity compared to existing methods.

Parallel implementation reduces decoding latency.

Abstract

A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The 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). To implement the matrix triangulation, we apply belief propagation decoding type operations. We also indicate how this decoder can be implemented in parallel for low latency decoding. Numerical simulations are used to evaluate the performance and computational complexity of the new algorithm.