Quantum Speedup for Polar Maximum Likelihood Decoding

TL;DR

This paper introduces a quantum decoding architecture for polar codes using Grover adaptive search, achieving maximum likelihood performance with quadratic speedup and supporting Gray-coded multi-level modulation.

Contribution

A novel quantum ML decoding method for polar codes based on Grover search, supporting multi-level modulation without increasing search complexity.

Findings

Achieves ML decoding performance for polar codes.

Provides quadratic speedup in query complexity.

Supports Gray-coded multi-level modulation.

Abstract

Conventional decoding algorithms for polar codes strive to balance achievable performance and computational complexity in classical computing. While maximum likelihood (ML) decoding guarantees optimal performance, its NP-hard nature makes it impractical for real-world systems. In this letter, we propose a novel ML decoding architecture for polar codes based on the Grover adaptive search, a quantum exhaustive search algorithm. Unlike conventional studies, our approach, enabled by a newly formulated objective function, uniquely supports Gray-coded multi-level modulation without expanding the search space size compared to the classical ML decoding. Simulation results demonstrate that our proposed quantum decoding achieves ML performance while providing a pure quadratic speedup in query complexity.