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Low-Density Parity-Check (LDPC) codes are a class of linear error-correcting codes that use a sparse bipartite graph to represent parity-check constraints, enabling efficient error correction with iterative decoding algorithms like belief propagation. They are widely used in modern communication systems due to their near-capacity performance and scalability for various block lengths and code rates.
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Low-Density Parity-Check (LDPC) codes are a class of error-correcting codes that enable reliable data transmission over noisy communication channels by using sparse bipartite graphs to represent parity-check matrices. They are known for their capacity-approaching performance and are widely used in modern communication systems, such as 5G and Wi-Fi, due to their efficient iterative decoding algorithms like belief propagation.
Low-density parity-check (LDPC) codes are a class of linear error-correcting codes that achieve near-optimal performance close to the Shannon limit, making them highly efficient for data transmission over noisy channels. They utilize sparse bipartite graphs for encoding and decoding, allowing for iterative algorithms that significantly reduce computational complexity.
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Gallager codes, also known as Low-Density Parity-Check (LDPC) codes, are a class of linear error-correcting codes that are defined by sparse bipartite graphs. They are known for their capacity-approaching performance on noisy channels and efficient decoding algorithms, making them highly effective in modern communication systems.
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Graphical models are a powerful framework for representing complex dependencies among random variables and building large-scale multivariate statistical models. They are widely used in machine learning and statistics to simplify the representation and computation of joint probability distributions through graph structures.
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Bayesian Networks are graphical models that represent probabilistic relationships among a set of variables using directed acyclic graphs, enabling reasoning under uncertainty. They are widely used for tasks such as prediction, diagnosis, and decision-making by leveraging conditional dependencies and Bayes' theorem.
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Sparse graph codes are a class of error-correcting codes that use graphs with a sparse structure to efficiently encode and decode information, enabling reliable communication over noisy channels. They leverage the sparsity of the graph to achieve low complexity in both encoding and decoding, making them highly suitable for modern communication systems.
Iterative decoding algorithms are techniques used in error correction for digital communication systems, where the decoder iteratively refines its estimates of the transmitted message by exchanging information between component decoders. These algorithms, such as the belief propagation and turbo decoding, significantly enhance the performance of error-correcting codes by leveraging the structure of the code to improve reliability and efficiency.
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Markov Random Fields (MRFs) are a type of probabilistic graphical model that represent the joint distribution of a set of random variables having a Markov property described by an undirected graph. They are particularly useful for modeling spatial dependencies and are widely used in image processing, computer vision, and statistical physics.
Soft-Input Soft-Output (SISO) decoding is a technique used in communication systems to improve error correction by taking into account the probability of received symbols and providing probabilistic information about the decoded output. This approach is essential in iterative decoding algorithms, such as Turbo codes and LDPC codes, where it refines the likelihood of bit values through multiple iterations to achieve near-optimal performance.
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LDPC (Low-Density Parity-Check) codes are a type of error-correcting code that allows for efficient data transmission over noisy communication channels by using a sparse bipartite graph to represent the parity-check matrix. They offer near Shannon-limit performance and are widely used in modern communication systems, such as 5G, Wi-Fi, and satellite communications, due to their excellent error correction capabilities and iterative decoding algorithms like belief propagation.
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Inference algorithms are computational procedures used to derive new information, conclusions, or predictions from existing data and models, often involving probabilistic or statistical techniques. They play a crucial role in machine learning, enabling systems to make decisions or understand patterns from inputs without explicit programming.
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Clique potentials are functions defined on subsets of variables, usually called cliques, in probabilistic graphical models. They represent local coherence or compatibility among the variables within a clique, influencing the joint distribution over the entire set of variables in the model.
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The Sum-Product Algorithm is an essential computational procedure for performing inference on probabilistic graphical models, particularly in factor graphs. It efficiently computes marginal distributions, leveraging the graph's structure to minimize redundant calculations and is fundamental in applications such as decoding error-correcting codes and Bayesian networks.
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Variable nodes are critical components in factor graphs where they represent variables and connect to factor nodes, participating in the process of probabilistic inference. By passing messages between nodes, they collaboratively update beliefs about the values of variables in applications such as decoding and computer vision.
Probabilistic Graphical Models (PGMs) are frameworks that leverage graph theory to succinctly capture the complex dependencies among random variables in probabilistic systems. By using nodes to represent variables and edges to depict conditional dependencies, PGMs enable efficient computation and inference, making them invaluable in domains such as machine learning, natural language processing, and computer vision.
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