Detection and Decoding: New Learning-Based Algorithms and Their Fundamental Limits

Abstract

The ever-increasing demand for low-latency, higher reliability, and enhanced coverage in next-generation mobile communications, particularly for applications such as the Internet of Things and autonomous driving, necessitates the development of new algorithms that improve performance or reduce the complexity of contemporary approaches. Achieving these objectives relies on advancements in areas such as low-complexity modulation, coding and decoding schemes, detection algorithms, and beamforming methods. This thesis aims to address these needs through innovations in machine learning for channel coding and detection. First, we theoretically investigate neural belief propagation (NBP) decoders' ability to enhance decoding performance. Our theoretical and empirical analysis reveals the dependence of NBP decoders' generalization capabilities on factors such as code parameters, decoding iterations, and training dataset size. These insights are crucial for optimizing the design and training of NBP decoders for practical applications. Second, we propose Sparse Matrix Codes (SMC), a novel channel coding technique tailored for ultra-reliable low-latency communications. SMC maps message bits to a sparse matrix, which is then multiplied by a spreading matrix and transmitted over the communication channel. By adopting tools from compressed sensing, we derive a low-complexity decoding algorithm to effectively recover the message from the channel output. Lastly, we introduce DRE-CUSUM, a machine learning-based change detection method for high-dimensional data with unknown distribution parameters. The core idea is to estimate the density ratio before and after a split point in a time series, using a non-parametric model to detect changes. We provide theoretical justification and accuracy guarantees for the proposed approach, highlighting its robustness and reliability.