Quantum error correction is necessary to protect logical quantum states and operations. However, no meaningful data protection can be made when the syndrome extraction is erroneous due to faulty measurement gates. Quantum datasyndrome (DS) codes are designed to protect the data qubits and syndrome bits concurrently. In this paper, we propose an efficient decoding algorithm for quantum DS codes with sparse check matrices. Based on a refined belief propagation (BP) decoding for stabilizer codes, we propose a DS-BP algorithm to handle the quaternary quantum data errors and binary syndrome bit errors. Moreover, a sparse quantum code may inherently be able to handle minor syndrome errors so that fewer redundant syndrome measurements are necessary. We demonstrate this with simulations on a quantum hypergraph-product code.
AV-HuBERT, a multi-modal self-supervised learning model, has been shown to be effective for categorical problems such as automatic speech recognition and lip-reading. This suggests that useful audio-visual speech representations can be obtained via utilizing multi-modal self-supervised embeddings. Nevertheless, it is unclear if such representations can be generalized to solve real-world multi-modal AV regression tasks, such as audio-visual speech enhancement (AVSE) and audio-visual speech separation (AVSS). In this study, we leveraged the pre-trained AV-HuBERT model followed by an SE module for AVSE and AVSS. Comparative experimental results demonstrate that our proposed model performs better than the state-of-the-art AVSE and traditional audio-only SE models. In summary, our results confirm the effectiveness of our proposed model for the AVSS task with proper fine-tuning strategies, demonstrating that multi-modal selfsupervised embeddings obtained from AV-HUBERT can be generalized to audio-visual regression tasks.
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