Error Correction Code for Future Communication Systems

Muhammad Imansyah Basudewa, Khoirul Anwar, Melinda Br Ginting

This paper proposes simple quantum [[9],[1],[3]] error correction codes for quantum systems beyond qubits, focusing on quantum ternary digits (qutrits) that represent the simplest higher-dimensional systems for future quantum technologies. Although qutrit-based systems offer larger capacity information over 2-dimensional systems, the challenge of identifying commuting stabilizers for constructing error correction codes becomes more difficult as the dimensionality increases or when working with a large number of qutrits. We design qutrit codes based on the generalized Pauli group and investigate the underlying structure, including shift, phase, and rotation operators. We successfully create suitable stabilizer codes that detect and correct qutrit errors. Furthermore, we (i) identify operators in qutrit, which are selected from various matrix interpretations for higher-dimensional systems, (ii) propose stabilizers for 9-qutrit error correction codes, and (iii) design a new 9-qutrit quantum circuit for communications. Our study is expected to contribute a foundational basis for possible future theoretical and experimental advancements in quantum computing, communications, and code-based cryptography in higher dimensional systems.

Imrane Chems Eddine Idrissi, Saïd Nouh, El Mehdi Bellfkih +2 more

Error-correcting codes and machine learning algorithms are two fundamental pillars in ensuring the reliability and accuracy of data transmission and storage systems. Error-correcting codes have long been instrumental in detecting and correcting errors during data communication and retrieval, while machine learning techniques have emerged as powerful tools for data analysis and pattern recognition. Integrating machine learning into error correction processes presents exciting opportunities to enhance error detection and correction performance, especially in complex and dynamic environments. In this article, we provide an in-depth overview of error-correcting codes, including traditional techniques like Hamming codes, Reed-Solomon codes, Turbo codes, and Convolutional codes. We explore the challenges faced by traditional error correction methods in handling modern data complexities. Subsequently, we delve into the integration of machine learning algorithms, such as neural networks, support vector machines, and decision trees, for error correction tasks. We discuss how machine learning enables adaptive, efficient, and dynamic error correction strategies. Furthermore, we examine real-world applications of machine learning-based error correction in communication systems, data storage, DNA sequencing, and quantum computing. Additionally, we highlight the challenges that researchers and engineers need to overcome, such as computational complexity, real-time processing, and adversarial attacks. Ultimately, the collaboration between error-correcting codes and machine learning offers exciting prospects for a future where data transmission and storage systems are more secure, efficient, and adaptable. By addressing challenges and embracing innovations, we can pave the way for error-free data management in an ever-evolving data-driven world.

Lehigh Preserve

Marco Chiani

Siddharth Kumar Das, Riccardo Bassoli, Frank H. P. Fitzek

Bridging the gap between classical and quantum communication is a well sought-after topic with significant potential in fortifying the networks of the future. In that direction, we have attempted to analyse realistic quantum channels through the lens of classical communication frameworks. To achieve this, we have developed a simulation environment that integrates classical link-level simulator with a quantum simulator, allowing an in-depth assessment of quantum noise impacts on 5G-compliant error correction code (ECC). We focused on the performance of low density parity check (LDPC) codes and polar codes under the influence of these quantum models. The comparative analysis, primarily on bit error rate (BER) performance demonstrates a clear advantage for LDPC codes across both quantum channel under identical simulation conditions. The results of this study offer valuable insights into how classical ECC perspectives can be applied to quantum channels, guiding the selection of appropriate error correction schemes tailored to specific quantum channel models.