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# Convolutional code

In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. [1]

58 relations: Adder (electronics), Algebraic normal form, Algorithm, Andrew Viterbi, BCJR algorithm, Bitwise operation, Block code, Boolean algebra, Cassini–Huygens, Claude Berrou, Communications satellite, Complexity, Concatenated error correction code, Convolution, Convolutional code, David J. C. MacKay, Degree of a polynomial, Digital video, Digital Video Broadcasting, Error floor, Exponential growth, Finite impulse response, Finite-state machine, Forward error correction, Hamming distance, Infinite impulse response, Intelsat, Linear time-invariant theory, Mars Exploration Rover, Mars Pathfinder, Maximum a posteriori estimation, Maximum likelihood estimation, Mobile telephony, Noisy-channel coding theorem, Peter Elias, Pioneer program, Polynomial code, Processor register, Puncturing, Quantum convolutional code, Rational function, Reed–Solomon error correction, Robert Fano, Sequential decoding, Serial concatenated convolutional codes, Shannon–Hartley theorem, SIMD, Soft output Viterbi algorithm, Systematic code, Telecommunication, ... Expand index (8 more) »

## Algebraic normal form

In Boolean algebra, the algebraic normal form (ANF), ring sum normal form (RSNF or RNF), Zhegalkin normal form, or Reed–Muller expansion is a way of writing logical formulas in one of three subforms.

## Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

## Andrew Viterbi

Andrew James Viterbi (born Andrea Giacomo Viterbi; March 9, 1935) is an Italian-born American electrical engineer and businessman who co-founded Qualcomm Inc. and invented the Viterbi algorithm.

## BCJR algorithm

The BCJR algorithm is an algorithm for maximum a posteriori decoding of error correcting codes defined on trellises (principally convolutional codes).

## Bitwise operation

In digital computer programming, a bitwise operation operates on one or more bit patterns or binary numerals at the level of their individual bits.

## Block code

In coding theory, a block code is any member of the large and important family of error-correcting codes that encode data in blocks.

## Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

## Cassini–Huygens

The Cassini–Huygens mission, commonly called Cassini, was a collaboration between NASA, the European Space Agency (ESA), and the Italian Space Agency (ASI) to send a probe to study the planet Saturn and its system, including its rings and natural satellites.

## Claude Berrou

Claude Berrou (born September 23, 1951 in Penmarch) is a French professor in electrical engineering at École Nationale Supérieure des Télécommunications de Bretagne, now IMT Atlantique.

## Communications satellite

A communications satellite is an artificial satellite that relays and amplifies radio telecommunications signals via a transponder; it creates a communication channel between a source transmitter and a receiver at different locations on Earth.

## Complexity

Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions.

## Concatenated error correction 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.

## Convolution

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

## Convolutional code

In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream.

## David J. C. MacKay

Sir David John Cameron MacKay (22 April 1967 – 14 April 2016) was a British physicist, mathematician, and academic.

## Degree of a polynomial

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

## Digital video

Digital video is an electronic representation of moving visual images (video) in the form of encoded digital data.

Digital Video Broadcasting (DVB) is a set of internationally open standards for digital television.

## Error floor

The error floor is a phenomenon encountered in modern iterated sparse graph-based error correcting codes like LDPC codes and turbo codes.

## Exponential growth

Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.

## Finite impulse response

In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time.

## Finite-state machine

A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation.

## Forward error correction

In 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.

## Hamming distance

In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.

## Infinite impulse response

Infinite impulse response (IIR) is a property applying to many linear time-invariant systems.

## Intelsat

Intelsat, S.A. is a communications satellite services provider.

## Linear time-invariant theory

Linear time-invariant theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas.

## Mars Exploration Rover

NASA's Mars Exploration Rover (MER) mission is an ongoing robotic space mission involving two Mars rovers, Spirit and Opportunity, exploring the planet Mars.

## Mars Pathfinder

Mars Pathfinder (MESUR Pathfinder) is an American robotic spacecraft that landed a base station with a roving probe on Mars in 1997.

## Maximum a posteriori estimation

In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution.

## Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.

## Mobile telephony

Mobile telephony is the provision of telephone services to phones which may move around freely rather than stay fixed in one location.

## Noisy-channel coding theorem

In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.

## Peter Elias

Peter Elias (November 23, 1923 – December 7, 2001) was a pioneer in the field of information theory.

## Pioneer program

The Pioneer program is a series of United States unmanned space missions that were designed for planetary exploration.

## Polynomial code

In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length) that are divisible by a given fixed polynomial (of shorter length, called the generator polynomial).

## Processor register

In computer architecture, a processor register is a quickly accessible location available to a computer's central processing unit (CPU).

## Puncturing

In coding theory, puncturing is the process of removing some of the parity bits after encoding with an error-correction code.

## Quantum convolutional code

Quantum block codes are useful in quantum computing and in quantum communications.

## Rational function

In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.

## Reed–Solomon error correction

Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960.

## Robert Fano

Roberto Mario "Robert" Fano (11 November 1917 – 13 July 2016) was an Italian-American computer scientist and professor of electrical engineering and computer science at the Massachusetts Institute of Technology.

## Sequential decoding

Sequential decoding is a limited memory technique for decoding tree codes.

## Serial concatenated convolutional codes

Serial concatenated convolutional codes (SCCC) are a class of forward error correction (FEC) codes highly suitable for turbo (iterative) decoding.

## Shannon–Hartley theorem

In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise.

## SIMD

Single instruction, multiple data (SIMD) is a class of parallel computers in Flynn's taxonomy.

## Soft output Viterbi algorithm

The soft output Viterbi algorithm (SOVA) is a variant of the classical Viterbi algorithm.

## Systematic code

In coding theory, a systematic code is any error-correcting code in which the input data is embedded in the encoded output.

## Telecommunication

Telecommunication is the transmission of signs, signals, messages, words, writings, images and sounds or information of any nature by wire, radio, optical or other electromagnetic systems.

## Transfer function

In engineering, a transfer function (also known as system function or network function) of an electronic or control system component is a mathematical function giving the corresponding output value for each possible value of the input to the device.

## Trellis (graph)

A trellis is a graph whose nodes are ordered into vertical slices (time), and with each node at each time connected to at least one node at an earlier and at least one node at a later time.

## Turbo code

In information theory, turbo codes (originally in French Turbocodes) are a class of high-performance forward error correction (FEC) codes developed around 1990–91 (but first published in 1993), which were the first practical codes to closely approach the channel capacity, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level.

## Very-large-scale integration

Very-large-scale integration (VLSI) is the process of creating an integrated circuit (IC) by combining hundreds of thousands of transistors or devices into a single chip.

## Viterbi algorithm

The Viterbi algorithm is a dynamic programming algorithm for finding the most likely sequence of hidden states&mdash;called the Viterbi path&mdash;that results in a sequence of observed events, especially in the context of Markov information sources and hidden Markov models.

## Voyager program

The Voyager program is an American scientific program that employs two robotic probes, Voyager 1 and Voyager 2, to study the outer Solar System.

## XOR gate

The XOR gate (sometimes EOR gate, or EXOR gate and pronounced as Exclusive OR gate) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd.

## Z-transform

In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation.

## References

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