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Error-correcting Codes With Feedback
In mathematics, computer science, telecommunication, information theory, and searching theory, error-correcting codes with feedback are error correcting codes designed to work in the presence of feedback from the receiver to the sender.See and . Problem Alice (the sender) wishes to send a value ''x'' to Bob (the receiver). The communication channel between Alice and Bob is imperfect, and can introduce errors. Solution An error-correcting code is a way of encoding ''x'' as a message such that Bob will successfully understand the value ''x'' as intended by Alice, even if the message Alice sends and the message Bob receives differ. In an error-correcting code with feedback, the channel is two-way: Bob can send feedback to Alice about the message he received. Noisy feedback In an error-correcting code without noisy feedback, the feedback received by the sender is always free of errors. In an error-correcting code with noisy feedback, errors can occur in the feedback, as w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of the Information Age. Shannon was the first to describe the use of Boolean algebra—essential to all digital electronic circuits—and helped found artificial intelligence (AI). Roboticist Rodney Brooks declared Shannon the 20th century engineer who contributed the most to 21st century technologies, and mathematician Solomon W. Golomb described his intellectual achievement as "one of the greatest of the twentieth century". At the University of Michigan, Shannon dual degreed, graduating with a Bachelor of Science in electrical engineering and another in mathematics, both in 1936. A 21-year-old master's degree student in electrical engineering at MIT, his thesis, "A Symbolic Analysis of Relay and Switching Circuits", demonstrated that electric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elwyn Berlekamp
Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.Elwyn Berlekamp listing at the Department of Mathematics, . Berlekamp was widely known for his work in computer science, and . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bar-Kochba Game
Simon bar Kokhba ( ) or Simon bar Koseba ( ), commonly referred to simply as Bar Kokhba, was a Jewish military leader in Judea. He lent his name to the Bar Kokhba revolt, which he initiated against the Roman Empire in 132 CE. Though they were ultimately unsuccessful, Bar Kokhba and his rebels did manage to establish and maintain a Jewish state for about three years after beginning the rebellion. Bar Kokhba served as the state's leader, crowning himself as '' nasi'' (). Some of the rabbinic scholars in his time believed him to be the long-expected Messiah. In 135, Bar Kokhba was killed by Roman troops in the fortified town of Betar The Betar Movement (), also spelled Beitar (), is a Revisionist Zionism, Revisionist Zionist youth movement founded in 1923 in Riga, Latvia, by Ze'ev Jabotinsky, Vladimir (Ze'ev) Jabotinsky. It was one of several right-wing youth movements tha .... The Judean rebels who remained after his death were all killed or enslaved within the next year, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfréd Rényi
Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory. Life Rényi was born in Budapest to Artúr Rényi and Borbála Alexander; his father was a mechanical engineer, while his mother was the daughter of philosopher and literary critic Bernhard Alexander; his uncle was Franz Alexander, a Hungarian-American psychoanalyst and physician. He was prevented from enrolling in university in 1939 due to the anti-Jewish laws then in force, but enrolled at the University of Budapest in 1940 and finished his studies in 1944. At this point, he was drafted to forced labour service, from which he managed to escape during transportation of his company. He was in hiding with false documents for six months. Biographers tell an incredible story about Rényi: after half of a year in hiding, he managed to get hold of a soldier's uniform and march ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memoryless
In probability and statistics, memorylessness is a property of probability distributions. It describes situations where previous failures or elapsed time does not affect future trials or further wait time. Only the geometric and exponential distributions are memoryless. Definition A random variable X is memoryless if \Pr(X>t+s \mid X>s)=\Pr(X>t)where \Pr is its probability mass function or probability density function when X is discrete or continuous respectively and t and s are nonnegative numbers. In discrete cases, the definition describes the first success in an infinite sequence of independent and identically distributed Bernoulli trials, like the number of coin flips until landing heads. In continuous situations, memorylessness models random phenomena, like the time between two earthquakes. The memorylessness property asserts that the number of previously failed trials or the elapsed time is independent, or has no effect, on the future trials or lead time. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Signal
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next. This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a new fixed reading of 10:38, etc. In this framework, each variable of interest is measured once at each time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable "time". A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Search Algorithm
In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the Feasible region, search space of a problem domain, with Continuous or discrete variable, either discrete or continuous values. Although Search engine (computing), search engines use search algorithms, they belong to the study of information retrieval, not algorithmics. The appropriate search algorithm to use often depends on the data structure being searched, and may also include prior knowledge about the data. Search algorithms can be made faster or more efficient by specially constructed database structures, such as search trees, hash maps, and database indexes. Search algorithms can be classified based on their mechanism of searching into three types of algorithms: linear, binary, and hashing. Linear search algorithms check every record for the one associated with a target key i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adaptive Algorithm
An adaptive algorithm is an algorithm that changes its behavior at the time it is run, based on information available and on ''a priori'' defined reward mechanism (or criterion). Such information could be the story of recently received data, information on the available computational resources, or other run-time acquired (or ''a priori'' known) information related to the environment in which it operates. Among the most used adaptive algorithms is the Widrow-Hoff’s least mean squares (LMS), which represents a class of stochastic gradient-descent algorithms used in adaptive filtering and machine learning. In adaptive filtering the LMS is used to mimic a desired filter by finding the filter coefficients that relate to producing the least mean square of the error signal (difference between the desired and the actual signal). For example, stable partition, using no additional memory is ''O''(''n'' lg ''n'') but given ''O''(''n'') memory, it can be ''O''(''n'') in time. As implemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-way Communication
Two-way communication is a form of transmission in which both parties involved transmit information. Two-way communication has also been referred to as interpersonal communication. Common forms of two-way communication are: * Amateur radio, CB or FRS radio contacts. * Chatrooms and instant messaging. * Computer networks. See backchannel. * In-person communication. * Telephone conversations. A cycle of communication and two-way communication are actually two different things. If we examine closely the anatomy of communication – the actual structure and parts – we will discover that a cycle of communication is not a two-way communication in its entirety. Meaning, two way communication is not as simple as one may infer. One can improve two-way or interpersonal communication by focusing on the eyes of the person speaking, making eye contact, watching body language, responding appropriately with comments, questions, and paraphrasing, and summarizing to confirm main points and an ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
