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arXiv · 2411.04727

Quantum Speedup for Polar Maximum Likelihood Decoding

Shintaro Fujiwara·Naoki Ishikawa
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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.

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Shintaro Fujiwara, Naoki Ishikawa. 2024-11-07. Quantum Speedup for Polar Maximum Likelihood Decoding. https://arxiv.org/abs/2411.04727

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