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EXIT Chart
An extrinsic information transfer chart, commonly called an EXIT chart, is a technique to aid the construction of good iteratively-decoded error-correcting codes (in particular low-density parity-check (LDPC) codes and Turbo codes). EXIT charts were developed by Stephan ten Brink, building on the concept of extrinsic information developed in the Turbo coding community.Stephan ten Brink, Convergence of Iterative Decoding, Electronics Letters, 35(10), May 1999 An EXIT chart includes the response of elements of decoder (for example a convolutional decoder of a Turbo code, the LDPC parity-check nodes or the LDPC variable nodes). The response can either be seen as extrinsic information or a representation of the messages in belief propagation. If there are two components which exchange messages, the behaviour of the decoder can be plotted on a two-dimensional chart. One component is plotted with its input on the horizontal axis and its output on the vertical axis. The other c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error-correcting Codes
In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code, or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors. Therefore a reverse channel to request re-transmission may not be needed. The cost is a fixed, higher forward channel bandwidth. The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code. FEC can be applied in situations where re-transmissions are costly or impossible, such as one-way communication links or when transmitting to multiple receivers in mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low-density Parity-check Code
Low-density parity-check (LDPC) codes are a class of error correction codes which (together with the closely-related turbo codes) have gained prominence in coding theory and information theory since the late 1990s. The codes today are widely used in applications ranging from wireless communications to flash-memory storage. Together with turbo codes, they sparked a revolution in coding theory, achieving order-of-magnitude improvements in performance compared to traditional error correction codes. Central to the performance of LDPC codes is their adaptability to the iterative belief propagation decoding algorithm. Under this algorithm, they can be designed to approach theoretical limits (Channel capacity, capacities) of many channels at low computation costs. Theoretically, analysis of LDPC codes focuses on sequences of codes of fixed code rate and increasing block length. These sequences are typically tailored to a set of channels. For appropriately designed sequences, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephan Ten Brink
Stephan may refer to: * Stephan, South Dakota, United States * Stephan (given name), a masculine given name * Stephan (surname), a Breton-language surname See also * Sankt-Stephan * Stefan (other) * Stephan-Oterma * Stephani * Stephen (other) Stephen is a masculine given name. Stephen may also refer to: People * Stephen (surname), including a list of people with the surname * Stephen (honorific), a South Slavic medieval honorific Places * Stephen, Minnesota, United States * Mount St ... * von Stephan {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extrinsic Information
In science and engineering, an intrinsic property is a property of a specified subject that exists itself or within the subject. An extrinsic property is not essential or inherent to the subject that is being characterized. For example, mass is an intrinsic property of any physical object, whereas weight is an extrinsic property that depends on the strength of the gravitational field in which the object is placed. Applications in science and engineering In materials science, an intrinsic property is independent of how much of a material is present and is independent of the form of the material, e.g., one large piece or a collection of small particles. Intrinsic properties are dependent mainly on the fundamental chemical composition and structure of the material. Extrinsic properties are differentiated as being dependent on the presence of avoidable chemical contaminants or structural defects. In biology, intrinsic effects originate from inside an organism or cell, such as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belief Propagation
Belief propagation, also known as sum–product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node (or variable), conditional on any observed nodes (or variables). Belief propagation is commonly used in artificial intelligence and information theory, and has demonstrated empirical success in numerous applications, including low-density parity-check codes, turbo codes, free energy approximation, and satisfiability. The algorithm was first proposed by Judea Pearl in 1982, who formulated it as an exact inference algorithm on trees, later extended to polytrees. While the algorithm is not exact on general graphs, it has been shown to be a useful approximate algorithm. Motivation Given a finite set of discrete random variables X_1, \ldots, X_n with joint probability mass function p, a common task is to compute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Erasure Channel
In coding theory and information theory, a binary erasure channel (BEC) is a communications channel model. A transmitter sends a bit (a zero or a one), and the receiver either receives the bit correctly, or with some probability P_e receives a message that the bit was not received ("erased") . Definition A binary erasure channel with erasure probability P_e is a channel with binary input, ternary output, and probability of erasure P_e. That is, let X be the transmitted random variable with alphabet \. Let Y be the received variable with alphabet \, where \text is the erasure symbol. Then, the channel is characterized by the conditional probabilities: :\begin \operatorname X = 0 &= 1 - P_e \\ \operatorname X = 1 &= 0 \\ \operatorname X = 0 &= 0 \\ \operatorname X = 1 &= 1 - P_e \\ \operatorname X = 0 &= P_e \\ \operatorname X = 1 &= P_e \end Capacity The channel capacity of a BEC is 1-P_e, attained with a uniform distribution for X (i.e. half of the inputs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Detection And Correction
In information theory and coding theory with applications in computer science and telecommunications, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Definitions ''Error detection'' is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. ''Error correction'' is the detection of errors and reconstruction of the original, error-free data. History In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
