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Binary Symmetric Channel
A binary symmetric channel (or BSCp) is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver will receive a bit. The bit will be "flipped" with a "crossover probability" of ''p'', and otherwise is received correctly. This model can be applied to varied communication channels such as telephone lines or disk drive storage. The noisy-channel coding theorem applies to BSCp, saying that information can be transmitted at any rate up to the channel capacity with arbitrarily low error. The channel capacity is 1 - \operatorname H_\text(p) bits, where \operatorname H_\text is the binary entropy function. Codes including Forney's code have been designed to transmit information efficiently across the channel. Definition A binary symmetric channel with crossover probability p, denoted by BSCp, is a channel with binary input and binary output and probability of error p. That i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communications Channel
A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for information transfer of, for example, a digital bit stream, from one or several ''senders'' to one or several '' receivers''. A channel has a certain capacity for transmitting information, often measured by its bandwidth in Hz or its data rate in bits per second. Communicating an information signal across distance requires some form of pathway or medium. These pathways, called communication channels, use two types of media: Transmission line (e.g. twisted-pair, coaxial, and fiber-optic cable) and broadcast (e.g. microwave, satellite, radio, and infrared). In information theory, a channel refers to a theoretical ''channel model'' with certain error characteristics. In this more general view, a storage device is also a communication channel, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to end th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduction (complexity)
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first. Intuitively, problem ''A'' is reducible to problem ''B'', if an algorithm for solving problem ''B'' efficiently (if it existed) could also be used as a subroutine to solve problem ''A'' efficiently. When this is true, solving ''A'' cannot be harder than solving ''B''. "Harder" means having a higher estimate of the required computational resources in a given context (e.g., higher time complexity, greater memory requirement, expensive need for extra hardware processor cores for a parallel solution compared to a single-threaded solution, etc.). The existence of a reduction from ''A'' to ''B'', can be written in the shorthand notation ''A'' ≤m ''B'', usually with a subscript on the ≤ to indicate the t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communication Theory
Communication theory is a proposed description of communication phenomena, the relationships among them, a storyline describing these relationships, and an argument for these three elements. Communication theory provides a way of talking about and analyzing key events, processes, and commitments that together form communication. Theory can be seen as a way to map the world and make it navigable; communication theory gives us tools to answer empirical, conceptual, or practical communication questions. Communication is defined in both commonsense and specialized ways. Communication theory emphasizes its symbolic and social process aspects as seen from two perspectives—as exchange of information (the transmission perspective), and as work done to connect and thus enable that exchange (the ritual perspective). Sociolinguistic research in the 1950s and 1960s demonstrated that the level to which people change their formality of their language depending on the social context that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Noise
In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects. In particular, noise is inherent in physics, and central to thermodynamics. Any conductor with electrical resistance will generate thermal noise inherently. The final elimination of thermal noise in electronics can only be achieved cryogenically, and even then quantum noise would remain inherent. Electronic noise is a common component of noise in signal processing. In communication systems, noise is an error or undesired random disturbance of a useful information signal in a communication channel. The noise is a summation of unwanted or disturbing energy from natural and sometimes man-made sources. Noise is, however, typically distinguished from interference, for example in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference ratio (SNIR) measu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cell Division
Cell division is the process by which a parent cell (biology), cell divides into two daughter cells. Cell division usually occurs as part of a larger cell cycle in which the cell grows and replicates its chromosome(s) before dividing. In eukaryotes, there are two distinct types of cell division: a vegetative division (mitosis), producing daughter cells genetically identical to the parent cell, and a cell division that produces Haploidisation, haploid gametes for sexual reproduction (meiosis), reducing the number of chromosomes from two of each type in the diploid parent cell to one of each type in the daughter cells. In cell biology, mitosis (Help:IPA/English, /maɪˈtoʊsɪs/) is a part of the cell cycle, in which, replicated chromosomes are separated into two new Cell nucleus, nuclei. Cell division gives rise to genetically identical cells in which the total number of chromosomes is maintained. In general, mitosis (division of the nucleus) is preceded by the S stage of interph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LDPC
In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel. An LDPC code is constructed using a sparse Tanner graph (subclass of the bipartite graph). LDPC codes are capacity-approaching codes, which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical maximum (the Shannon limit) for a symmetric memoryless channel. The noise threshold defines an upper bound for the channel noise, up to which the probability of lost information can be made as small as desired. Using iterative belief propagation techniques, LDPC codes can be decoded in time linear to their block length. LDPC codes are finding increasing use in applications requiring reliable and highly efficient information transfer over bandwidth-constrained or return-channel-constrained links in the presence of corrupting noise. Implementation of LDPC codes has lag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf. syndrome decoding). Linear codes are used in forward error correction and are applied in methods for transmitting symbols (e.g., bits) on a communications channel so that, if errors occur in the communication, some errors can be corrected or detected by the recipient of a message block. The codewords in a linear block code are blocks of symbols that are encoded using more symbols than the original value to be sent. A linear code of length ''n'' transmits blocks containing ''n'' symbols. For example, the ,4,3 Hamming code is a linear binary code which represents 4-bit messages using 7-bit codewords. Two distinct c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Linear Code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf. syndrome decoding). Linear codes are used in forward error correction and are applied in methods for transmitting symbols (e.g., bits) on a communications channel so that, if errors occur in the communication, some errors can be corrected or detected by the recipient of a message block. The codewords in a linear block code are blocks of symbols that are encoded using more symbols than the original value to be sent. A linear code of length ''n'' transmits blocks containing ''n'' symbols. For example, the ,4,3Hamming code is a linear binary code which represents 4-bit messages using 7-bit codewords. Two distinct codew ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concatenated Code
In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. They were conceived in 1966 by Dave Forney as a solution to the problem of finding a code that has both exponentially decreasing error probability with increasing block length and polynomial-time decoding complexity. Concatenated codes became widely used in space communications in the 1970s. Background The field of channel coding is concerned with sending a stream of data at the highest possible rate over a given communications channel, and then decoding the original data reliably at the receiver, using encoding and decoding algorithms that are feasible to implement in a given technology. Shannon's channel coding theorem shows that over many common channels there exist channel coding schemes that are able to transmit data reliably at all rates R less than a certain threshold C, called the channel capacity of the given channel. In fact, the ... [...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] |
Code
In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication channel or storage in a storage medium. An early example is an invention of language, which enabled a person, through speech, to communicate what they thought, saw, heard, or felt to others. But speech limits the range of communication to the distance a voice can carry and limits the audience to those present when the speech is uttered. The invention of writing, which converted spoken language into visual symbols, extended the range of communication across space and time. The process of encoding converts information from a source into symbols for communication or storage. Decoding is the reverse process, converting code symbols back into a form that the recipient understands, such as English or/and Spanish. One reason for coding is to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
