167 research outputs found

    Decoding of Non-Binary LDPC Codes Using the Information Bottleneck Method

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    Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information maximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to non-binary codes. This is not a straightforward extension, but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the log-max decoding algorithm and operates close to sum-product decoding.Comment: This paper has been presented at IEEE International Conference on Communications (ICC'19) in Shangha

    Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View

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    These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory, highlighting connections with statistical mechanics. We also stress common concepts with other disciplines dealing with similar problems that can be generically referred to as `large graphical models'. While most of the lectures are devoted to the classical channel coding problem over simple memoryless channels, we present a discussion of more complex channel models. We conclude with an overview of the main open challenges in the field.Comment: Lectures at Les Houches Summer School on `Complex Systems', July 2006, 44 pages, 25 ps figure

    Soft-Decoding-Based Strategies for Relay and Interference Channels: Analysis and Achievable Rates Using LDPC Codes

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    We provide a rigorous mathematical analysis of two communication strategies: soft decode-and-forward (soft-DF) for relay channels, and soft partial interference-cancelation (soft-IC) for interference channels. Both strategies involve soft estimation, which assists the decoding process. We consider LDPC codes, not because of their practical benefits, but because of their analytic tractability, which enables an asymptotic analysis similar to random coding methods of information theory. Unlike some works on the closely-related demodulate-and-forward, we assume non-memoryless, code-structure-aware estimation. With soft-DF, we develop {\it simultaneous density evolution} to bound the decoding error probability at the destination. This result applies to erasure relay channels. In one variant of soft-DF, the relay applies Wyner-Ziv coding to enhance its communication with the destination, borrowing from compress-and-forward. To analyze soft-IC, we adapt existing techniques for iterative multiuser detection, and focus on binary-input additive white Gaussian noise (BIAWGN) interference channels. We prove that optimal point-to-point codes are unsuitable for soft-IC, as well as for all strategies that apply partial decoding to improve upon single-user detection (SUD) and multiuser detection (MUD), including Han-Kobayashi (HK).Comment: Accepted to the IEEE Transactions on Information Theory. This is a major revision of a paper originally submitted in August 201
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