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Chronometry is the science of measuring time with high precision, essential for various fields such as astronomy, navigation, and physics. It involves the development and use of timekeeping devices and techniques to ensure accurate and consistent time measurement and synchronization.
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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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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.
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A bipartite graph is a type of graph in which vertices can be divided into two distinct sets such that no two vertices within the same set are adjacent. This structure is widely used in modeling relationships between two different classes of objects, like in matching problems and network flow algorithms.
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Error-correcting codes are essential for ensuring accurate data transmission over noisy channels by detecting and correcting errors without needing retransmission. They are widely used in digital communication systems, data storage, and computer networks to enhance reliability and efficiency.
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Channel capacity is the maximum rate at which information can be reliably transmitted over a communication channel, as defined by Shannon's noisy channel coding theorem. It represents the upper bound of data transmission efficiency, taking into account noise and interference in the channel.
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Iterative decoding is a process used in error correction for digital communication systems, where multiple rounds of decoding are performed to progressively improve the accuracy of the received message. By iteratively refining the estimates of transmitted data, it leverages techniques like belief propagation and turbo decoding to approach the Shannon limit of channel capacity.
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Belief propagation is an algorithm used for performing inference on graphical models, such as Bayesian networks and Markov random fields, by iteratively updating and passing messages between nodes. It is particularly effective for computing marginal distributions and finding the most probable configurations in tree-structured graphs, but can also be applied to loopy graphs with approximate results.
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The Shannon Limit, also known as the Shannon Capacity, is a fundamental theorem in information theory that defines the maximum rate at which information can be transmitted over a communication channel without error, given the presence of noise. It establishes the theoretical boundary for data transmission efficiency, influencing the design of modern communication systems by highlighting the trade-off between bandwidth, noise, and data rate.
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Information theory is a mathematical framework for quantifying information, primarily focusing on data compression and transmission efficiency. It introduces fundamental concepts such as entropy, which measures the uncertainty in a set of outcomes, and channel capacity, which defines the maximum rate of reliable communication over a noisy channel.
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Coding Theory is a branch of mathematics and computer science focused on the design of error-detecting and error-correcting codes to ensure reliable data transmission over noisy communication channels. It plays a crucial role in digital communication systems, data storage, and network security by optimizing data encoding and decoding processes to minimize errors and enhance efficiency.
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