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Error-correcting Codes With Feedback
In mathematics, computer science, telecommunication, information theory, and searching theory, error-correcting codes with feedback refers to 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts Institute of Technology (MIT), he wrote A Symbolic Analysis of Relay and Switching Circuits, his thesis demonstrating that electrical applications of Boolean algebra could construct any logical numerical relationship. Shannon contributed to the field of cryptanalysis for national defense of the United States during World War II, including his fundamental work on codebreaking and secure telecommunications. Biography Childhood The Shannon family lived in Gaylord, Michigan, and Claude was born in a hospital in nearby Petoskey, Michigan, Petoskey. His father, Claude Sr. (1862–1934), was a businessman and for a while, a judge of probate in Gaylord. His mother, Mabel Wolf Shannon (1890–1945), ... [...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.Contributors, ''IEEE Transactions on Information Theory'' 42, #3 (May 1996), p. 1048. DO10.1109/TIT.1996.490574Elwyn Berlekamp listing at the Department of Mathematics, . Berlekamp was widely known for his work in computer science, and |
Bar-Kochba Game
Simon ben Koseba or Cosiba ( he, שִׁמְעוֹן בַּר כֹסֵבָא, translit= Šīmʾōn bar Ḵōsēḇaʾ ; died 135 CE), commonly known as Bar Kokhba ( he, שִׁמְעוֹן בַּר כּוֹכְבָא, translit=Šīmʾōn bar Kōḵḇāʾ ), was a Jewish military leader who led the Bar Kokhba revolt against the Roman Empire in 132 CE. The revolt established a three-year-long independent Jewish state in which Bar Kokhba ruled as ''nasi'' ("prince"). Some of the rabbinic scholars in his time imagined him to be the long-expected Messiah. Bar Kokhba fell in the fortified town of Betar. Name Documented name Documents discovered in the 20th century in the Cave of Letters give his original name, with variations: Simeon bar Kosevah (), Bar Kosevaʾ () or Ben Kosevaʾ (). It is probable that his original name was Bar Koseba. The name may indicate that his father or his place of origin was named Koseva(h), with Khirbet Kuwayzibah being a likely nominee for id ... [...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 escaped. He then completed his PhD in 1947 at the University of Szeged, under the advisement of Frigyes Riesz. He married Katalin Schulhof (who used Kató Rényi as her married name), herself a mathematician, in 1946; their daughter Zsuzsanna was bor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memoryless
In probability and statistics, memorylessness is a property of certain probability distributions. It usually refers to the cases when the distribution of a "waiting time" until a certain event does not depend on how much time has elapsed already. To model memoryless situations accurately, we must constantly 'forget' which state the system is in: the probabilities would not be influenced by the history of the process. Only two kinds of distributions are memoryless: geometric distributions of non-negative integers and the exponential distributions of non-negative real numbers. In the context of Markov processes, memorylessness refers to the Markov property, an even stronger assumption which implies that the properties of random variables related to the future depend only on relevant information about the current time, not on information from further in the past. The present article describes the use outside the Markov property. Waiting time examples With memory Most phenomena are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Signal
In Dynamical system, mathematical dynamics, discrete time and continuous time are two alternative frameworks within which Variable (mathematics), 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 ... [...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 search space of a problem domain, with either discrete or continuous values. algorithms are Although search engines use search algorithms, they belong to the study of information retrieval, not algorithmics. The appropriate search algorithm 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 in a linear fashion. Binary, or half-interval, searches repeatedly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. 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 for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...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 implement ... [...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] |
