Applications of LDPC Codes to RF-Optical Hybrid Systems and the Line Product Code
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Applications of LDPC Codes to RF-Optical Hybrid Systems and the Line Product Code


This thesis consists of an introduction, four main sections, and conclusion. The introduction gives a quick overview of communication channels and the basics of message passing algorithms. The first section focuses on the challenges of communicating over a fading channel using optical transmitters and receivers. Recognizing the limitations of a purely optical transmission system during environmental fades, the section proposes a hybrid RF-Optical system. The hybrid system consists of a high-throughput optical link closed by a Low Density Parity Check (LDPC) code alongside a separate RF link. The section proposes two different architectures for a hybrid system with varying degrees of mixing between the two links. For each architecture, their performance was evaluated during on a simulated fading channel and Additive White Gaussian Noise (AWGN) channel.The second section of this thesis capitalizes on the recent advancements in deep learning and applies it to the most popular LDPC decoding process known as message passing. The section first deconstructs the steps of message passing into nodes that can be interpreted as a type of Neural Network. Then, utilizing gradient descent methods including Adaptive Movement Estimation (ADAM), multiplicative weights for message passing are found and optimized. The key contribution of the section is the connection between these multiplicative weights and properties intrinsic to the LDPC code structure. By exploiting this relationship, a weight-sharing paradigm based on node degree is proposed, resulting in a Neural-Normalized MinSum (N-NMS) decoder which dramatically reduces the complexity of both training and implementation compared to typical neural network based decoders. The third section discusses a unique case study involving the Consultative Committee for Space Data Systems (CCSDS) 141.11-O-1 Line Product Code (LPC). Being such a short block-length code, two Maximum Likelihood (ML) decoders were evaluated against message passing decoders including MinSum (MS), Belief Propagation (BP), and Neural-Normalized MinSum (N-NMS). Analysis was carried out considering both the decoding performance and resulting hardware complexity of the decoders. Continuing on this, the fourth and final section aims to give additional insight as to why the N-NMS decoder performed so well on the LPC. This section proposes that the unique graph structure of the LPC allowed for key optimizations such as breaking length-4 cycles that the N-NMS training process capitalized on during its training.

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