Polar codes encounter challenges in decoder complexity while preserving good error-correction properties. Instead of conventional decoders, a quantum annealer (QA) decoder has been proposed to explore untapped possibilities. For future QA applications, a crucial prerequisite is transforming the optimization problem into quadratic unconstrained binary optimization (QUBO) form. However, existing QUBO forms for polar decoding result in suboptimal frame error rate (FER) performance for codes exceeding 8 bits. This paper redesigns the QUBO form for polar decoding. We first introduce a novel receiver constraint modeled by the binary cross-entropy (BCE) function. Utilizing a simulated annealing (SA) solver with the proposed QUBO form with BCE (QUBO-BCE) achieves maximum-likelihood (ML) performance for a code length of 32 bits. Next, to reduce the number of variables, we remove the frozen variables and introduce a simplified QUBO-BCE form (SQUBO-BCE). Additionally, CRC polynomials are modelled into constraints in QUBO form, resulting in a CRC-aided SQUBO-BCE (CA-SQUBO-BCE) form for polar decoding to further enhance the FER. Numerical results demonstrate that SQUBO-BCE achieves ML performance and reduces up to 61.5% of variables compared to QUBO-BCE. Furthermore, the proposed CA-SQUBO-BCE achieves near CRC-aided ML performance. The proposed SQUBO-BCE requires the lowest number of SA processes to reach a specific FER.
Polar codes encounter challenges in decoder complexity while preserving good error-correction properties. Instead of conventional decoders, a quantum annealer (QA) decoder has been proposed to explore untapped possibilities. For future QA applications, a crucial prerequisite is transforming the optimization problem into quadratic unconstrained binary optimization (QUBO) form. However, existing QUBO forms for polar decoding result in suboptimal frame error rate (FER) performance for codes exceeding 8 bits. This paper redesigns the QUBO form for polar decoding. We first introduce a novel receiver constraint modeled by the binary cross-entropy (BCE) function. Utilizing a simulated annealing (SA) solver with the proposed QUBO form with BCE (QUBO-BCE) achieves maximum-likelihood (ML) performance for a code length of 32 bits. Next, to reduce the number of variables, we remove the frozen variables and introduce a simplified QUBO-BCE form (SQUBO-BCE). Additionally, CRC polynomials are modelled into constraints in QUBO form, resulting in a CRC-aided SQUBO-BCE (CA-SQUBO-BCE) form for polar decoding to further enhance the FER. Numerical results demonstrate that SQUBO-BCE achieves ML performance and reduces up to 61.5% of variables compared to QUBO-BCE. Furthermore, the proposed CA-SQUBO-BCE achieves near CRC-aided ML performance. The proposed SQUBO-BCE requires the lowest number of SA processes to reach a specific FER.
Polar decoders such as successive-cancellation and successive-cancellation list decoders are limited by their sequential nature, which leads to a linear increase in latency with the codeword length. Heuristic based decoders such as quantum annealing have been proposed to overcome this limitation. However, these decoders have shown poor performance when decoding polar codes with more than eight bits. In this paper, we developed new meta-heuristic based polar decoder, called xSA, which uses a new receiver constraint modeled by the binary cross-entropy function. We also propose a method to determine the weights used in a quadratic unconstrained binary optimization (QUBO) function. The polar code is assumed to have been sent across an AWGN channel and we conducted our experiments and simulations using PyQUBO and dwave-neal. Our results show that xSA is able to decode codes of length 16 and 32 with a near-ML FER performance, presenting itself as a promising alternative to traditional polar decoders for real world applications and next generation cellular communications.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. How- ever, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transfor- mations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated An- nealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total num- ber of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
Recent advances in quantum computing have shown great potential for solving combinatorial optimization problems. A notable example is the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum-inspired algorithms require Quadratic Unconstrained Binary Optimization (QUBO) formulations. Transforming constrained optimization into QUBO impacts the algorithms' speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess them by using Simulated Annealing (SA), and find that three of our approaches outperform existing methods in terms of execution time as well as quality and quantity of feasible solutions found. Also, we tested these transformations on a quantum annealer, which was unable to solve even small instances, due to limitations in connectivity and error rates. In general, our results highlight the advantages of the new approaches, which reduce the number of variables in the QUBO representation.
A new decoding scheme aided by simulated annealing algorithm is proposed to further improve the decoding performance of successive cancellation (SC) for polar codes at the short block. We use simulated annealing to revise the decoding result of SC which cannot pass the CRC check. To generate the new neighbors, the decoder flips one bit from the set of the least unreliable information bits each time in the estimated source vector of SC decoding. Euclidean distance is used to measure the gap between the new neighbor solution and the received word so that the decoder can obtain a global optimal solution. Simulation shows that the proposed decoder has a performance gain about 0.5 dB in terms of frame error rate (FER) under short blocks in the additive white Gaussian noise (AWGN) channel compared to other basic decoders, while keeping a low time cost through a parameter tuning process.