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Design, Automation, and Test in Europe

Practical MU-MIMO Detection and LDPC Decoding Through Digital Annealing

Po-Shao Chen, Wei Tang, Zhengya Zhang

Published Mar 31, 2025• 0 citations
Publisher

Abstract

Digital annealing has been successfully applied to solving combinatorial optimization (CO) problems. It is more flexible, robust, and easier to deploy on edge platforms compared to its counterparts including quantum annealing and analog and in-memory Ising machines. In this work, we apply digital annealing to compute-intensive communication digital signal processing problems, including multi-user detection in multiple-input and multiple-output (MU-MIMO) wireless communication systems and decoding low-density parity-check (LDPC) codes. We show that digital annealing can achieve near maximum likelihood (ML) accuracy for MIMO detection with even lower complexity than the conventional minimum mean square error (MMSE) detection. In LDPC decoding, we enhance digital annealing by introducing a new cost function that improves decoding accuracy and reduces computational complexity compared to the standard formulations.

DOI
10.23919/date64628.2025.10992822

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Digital annealing has been successfully applied to solving combinatorial optimization (CO) problems. It is more flexible, robust, and easier to deploy on edge platforms compared to its counterparts including quantum annealing and analog and in-memory Ising machines. In this work, we apply digital annealing to compute-intensive communication digital signal processing problems, including multi-user detection in multiple-input and multiple-output (MU-MIMO) wireless communication systems and decoding low-density parity-check (LDPC) codes. We show that digital annealing can achieve near maximum likelihood (ML) accuracy for MIMO detection with even lower complexity than the conventional minimum mean square error (MMSE) detection. In LDPC decoding, we enhance digital annealing by introducing a new cost function that improves decoding accuracy and reduces computational complexity compared to the standard formulations.
This paper introduces a deep unfolding-assisted proximal decoding for low-density parity-check (LDPC) codes. Proximal decoding method is a decoding algorithm based on the proximal gradient method. Our proposal, deep unfolding-assisted proximal (DU-Proximal) decoding, is obtained by applying deep unfolding to the proximal decoding. We especially focus on the decoding performance in multiple-input multiple-output (MIMO) channels. In numerical experiments, we compare the error correcting capability of the proposed algorithm with the minimum mean squared error (MMSE) signal detection method, the tanh signal detection method, and the MMSE jointly with belief propagation (BP) algorithm for LDPC decoding. The experimental results demonstrate that parameter optimization via DU yields significant performance gains, especially at high signal-to-noise ratio levels.
In the forthcoming 6G era, driven by the escalating demands for enhanced performance and reliability in communication systems, Low-Density Parity-Check (LDPC) codes emerge as a robust error correction coding scheme poised to effectively meet these requirements. In recent years, with the advancement of quantum computing, a proposal has emerged to integrate classical and quantum computing for the decoding of LDPC. The LDPC decoding can be treated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, thereby allowing the utilization of the D-Wave 2000Q quantum annealer for solving it. Expanding on this groundwork, the paper proposes an approach to enhance quantum annealing performance using classical algorithms. Specifically, it involves performing quantum annealing on the problem first, followed by post-processed using Maximum Likelihood Estimation (MLE) for the multiple outputs, known as QAML. Furthermore, to fully exploit the advantages of quantum annealing, this paper incorporates the energy and frequency of occurrence of candidate codewords as prior information into the Maximum Likelihood Estimation. These are called QAMLE and QAMLF respectively, further enhancing decoding performance. The proposed method is evaluated and compared with direct Quantum Annealing (QA) and Quantum Annealing with post-processing using Minimum Distance (QAMD). Research findings indicate that QAML exhibits a lower bit error rate compared to QA and QAMD.
Multi-user (MU), multiple-input, multiple-output (MIMO) detection has been extensively investigated, and many techniques have been proposed. However, further performance improvements may be constrained by limitations in classical computation. The motivation for this work is to test whether a machine that exploits quantum principles can offer improved performance over conventional detection approaches. This paper presents an evaluation of MIMO detection based on quantum annealing (QA) when run on an actual QA quantum processing unit (QPU) and describes the challenges and potential improvements. The evaluations show promising results in some cases, such as near-optimality in a QPSK-modulated 8×8 MIMO case, but poor results in other cases, such as for larger systems or when using 16-QAM. We show that some challenges of QA detection include dealing with integrated control errors (ICE), the limited dynamic range of QA QPUs, an exponential increase in the number of qubits to the problem size, and a high computation overhead. Solving these challenges could make QA-based detection superior to conventional approaches and bring a new generation of MU-MIMO detection methods.
We formulate maximum likelihood (ML) channel decoding as a quadratic unconstraint binary optimization (QUBO) and simulate the decoding by the current commercial quantum annealing machine, D-Wave 2000Q. We prepared two implementations with Ising model formulations, generated from the generator matrix and the parity-check matrix respectively. We evaluated these implementations of ML decoding for low-density parity-check (LDPC) codes, analyzing the number of spins and connections and comparing the decoding performance with belief propagation (BP) decoding and brute-force ML decoding with classical computers. The results show that these implementations are superior to BP decoding in relatively short length codes, and while the performance in the long length codes deteriorates, the implementation from the parity-check matrix formulation still works up to 1k length with fewer spins and connections than that of the generator matrix formulation due to the sparseness of parity-check matrices of LDPC.
An improved decoding algorithm,which aims to reduce the decoding complexity of irregular low-density parity-check(LDPC) codes,is presented for implementation with digital signal processors(DSPs) with reduced computation complexity and low error floor.The algorithm uses the modified min-sum(MMS) algorithm for check node processing with the extrinsic information updated sequentially, so that it exhibits a low decoding threshold with a limited number of iterations,while reducing the node processing complexity and error floor.Tests with a fixed-point DSP show that the algorithm achieves a low error floor and low decoding threshold with low implementation complexity.
Quantum and Classical computers continue to work together in tight cooperation to solve difficult problems. The combination is thus suggested in recent times for decoding the Low Density Parity Check (LDPC) codes, for the next generation Wireless Communication systems. In this paper we have worked out the Quadratic Unconstrained Binary Optimization (QUBO) formulation for Rayleigh Fading channels for two different scenarios- channel state fully known and not known. The resultant QUBO are solved using D-Wave 2000Q Quantum Annealer and the outputs from the Annealer are classically postprocessed, invoking the notion of diversity. Simple minimum distance decoding of the available copies of the outputs led to improved performance, compared to picking the minimum-energy solution in terms of Bit Error Rate (BER). Apart from providing these results and the comparisons to fully classical Simulated Annealing (SA) and the traditional Belief Propagation (BP) based strategies, some remarks about diversity due to quantum processing are also spelt out.