Quantum Speedup for Polar Maximum Likelihood Decoding

TL;DR

A novel ML decoding architecture for polar codes based on the Grover adaptive search, a quantum exhaustive search algorithm, that uniquely supports Gray-coded multi-level modulation without expanding the search space size compared to the classical ML decoding.

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.

Figures (6)

• Figure 1: System model of our proposed ML decoding architecture with GAS for polar codes.
• Figure 2: Quantum circuit for preparing a initial state for BPSK modulation.
• Figure 3: Quantum circuit for preparing the initial state for $4$-PAM.
• Figure 4: BLER performance comparisons of the conventional exhaustive search and the proposed quantum ML decoding.
• Figure 5: CDF of the number of iterations required to reach an optimal solution with ML decoding when $(N,K)=(16,8)$ and BPSK modulation is applied.