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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
Concatenated error correction code
Concatenated_error_correction_code
Scheme for controlling errors in data over noisy communication channels
information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over
Error_correction_code
Reliable digital data delivery methods on unreliable channels
information theory and coding theory with applications in computer science and telecommunications, error detection and correction (EDAC) or error control are techniques
Error detection and correction
Error_detection_and_correction
Process in quantum computing
Quantum error correction (QEC) comprises a set of techniques used in quantum memory and quantum computing to protect quantum information from errors arising
Quantum_error_correction
Error-correcting codes
algorithm. In 1977, Reed–Solomon codes were implemented in the Voyager program in the form of concatenated error correction codes. The first commercial application
Reed–Solomon_error_correction
Linear error correcting code
(LDPC) codes, also known as Gallager codes, are a class of error-correction codes first proposed in 1960. Together with the closely related turbo codes, they
Low-density_parity-check_code
High-performance forward error correction codes
In information theory, turbo codes are a class of high-performance forward error correction (FEC) codes developed around 1990–91, but first published in
Turbo_code
Ordering of binary values, used for positioning and error correction
instead of two. Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications
Gray_code
Simple but inefficient error-correcting code
(ARA) codes, allows for surprisingly good error correction performance. Repetition codes are one of the few known codes whose code rate can be automatically
Repetition_code
System of rules to convert information into another form or representation
has media related to Codes. ADDML Asemic writing Cipher Code (semiotics) Cultural code Equipment codes Quantum error correction Semiotics Universal language
Code
Serial concatenated convolutional codes (SCCC) are a class of forward error correction (FEC) codes highly suitable for turbo (iterative) decoding. Data
Serial concatenated convolutional codes
Serial_concatenated_convolutional_codes
Set of codewords, none a prefix of another
channel coding (including error correction) before transmission. For every uniquely decodable code there is a prefix code that has the same code word lengths
Prefix_code
Type of error-correcting code using convolution
Viterbi-decoded codes, usually concatenated with large Reed–Solomon error correction codes that steepen the overall bit-error-rate curve and produce extremely
Convolutional_code
Code used in quantum error correction
In quantum computing, the Shor code or Shor nine qubit code is a foundational code in quantum error correction that protects quantum information against
Shor_code
Error-correcting code
constant alphabet size. Before the Justesen error correction code was discovered, no error correction code was known that had all of these three parameters
Justesen_code
Quantum error correcting code
The Gottesman–Kitaev–Preskill (GKP) code is a quantum error correcting code that encodes logical qubits into the continuous degrees of freedom of a quantum
Gottesman–Kitaev–Preskill code
Gottesman–Kitaev–Preskill_code
Fountain code class
decoding Raptor codes. In a concatenated approach, the inner code is decoded first, using a belief propagation algorithm, as used for the LT codes. Decoding
Raptor_code
Error-correcting codes used in wireless communication
communication. In cryptography, duplicated Reed–Muller codes are concatenated with shortened Reed–Solomon codes in the Hamming Quasi-Cyclic (HQC) key encapsulation
Reed–Muller_code
Error-correcting codes used on compact discs
Reed–Solomon code (CIRC) provides error detection and error correction. CIRC adds to every three data bytes one redundant parity byte. Reed–Solomon codes are specifically
Cross-interleaved Reed–Solomon coding
Cross-interleaved_Reed–Solomon_coding
which is based on using an errors-and-erasures decoder for the outer code. A naive decoding algorithm for concatenated codes can not be an optimal way
Generalized minimum-distance decoding
Generalized_minimum-distance_decoding
Method of encoding digital data on multiple carrier frequencies
classical type of error correction coding used with OFDM-based systems is convolutional coding, often concatenated with Reed-Solomon coding. Usually, additional
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Proposed approach to a large-scale quantum computer based on Schrödinger cat states
A.; Chen, Cliff (2025-02-26). "Hardware‑efficient quantum error correction via concatenated bosonic qubits". Nature. 638 (8052): 927–934. arXiv:2409.13025
Cat_qubit_quantum_computer
Data storage technology
named RAID 5. Around 1988, the Thinking Machines' DataVault used error correction codes (now known as RAID 2) in an array of disk drives. A similar approach
RAID
Concept in coding theory
Ping, Li; Huang, Xiaoling; Phamdo, Nam (2001), "Zigzag codes and concatenated zigzag codes", IEEE Transactions on Information Theory, 47 (2): 800–807
Zigzag_code
Digital satellite television standard
DVB-S receivers). Improved coding: a modern large LDPC code is concatenated with an outer BCH code to achieve quasi-error-free (QEF) reception conditions
DVB-S2
Finds likely sequence of hidden states
processing framework provides the C++ implementation for Forward error correction codes and channel equalization here. C++ Java Archived 2014-05-04 at the
Viterbi_algorithm
File with the content of other files plus associated metadata
associated metadata such as file name, directory structure, error detection and correction information, and commentary. An archive file is often used to
Archive_file
Type of modem
Reed–Solomon codes usually concatenated with convolutional codes with an interleaving; New modems support superior error correction codes (turbo codes and LDPC
Satellite_modem
Digital radio standard
communication systems. A choice of audio codec, modulation and error-correction coding schemes and first trial broadcasts were made in 1990. A significant
Digital_Audio_Broadcasting
Quantum state, of opposed conditions
Quantum Computing) (2025-02-26). "Hardware-efficient quantum error correction via concatenated bosonic qubits". Nature. 638 (8052): 927–935. arXiv:2409.13025
Cat_state
Type of error-correcting code
a higher capacity for error correction. (The Hadamard code falls under the general umbrella of forward error correction, and just happens to be locally
Locally_decodable_code
methods Error detection and correction Forward error correction Andre Neubauer; Jurgen Freudenberger; Volker Kuhn (22 October 2007). Coding Theory.:
Soft-in_soft-out_decoder
Important algorithms in numerical statistics
compute the central moments of the concatenated time-history. Finally, the statistical moments of the concatenated history are computed from the central
Algorithms for calculating variance
Algorithms_for_calculating_variance
Theorem in quantum computing
quantum error correcting code can have a continuous symmetry which acts transversely on physical qubits". In other words, no quantum error correcting code can
Eastin–Knill_theorem
Standardized protocol
error correction and Automatic Protection Switching messages (e.g., alarms and maintenance messages) as may be required within the network. The error
Synchronous optical networking
Synchronous_optical_networking
Sending data method
done was ensuring correct decoding for up to d/2 errors, where d was the Hamming distance of the code. The problem with doing it this way is that it does
Computationally bounded adversary
Computationally_bounded_adversary
Reference model for network communication
coaxial cables), includes a complete data link layer that provides both error correction and flow control by means of a selective-repeat sliding-window protocol
OSI_model
Approach to software development
false starts and corrections usually occur before a satisfactory endpoint is reached in the worst case, the original state of the code may be irretrievably
Programming_by_permutation
American mobile digital TV standard
ATSC-M/H combines multiple error protection mechanisms for added robustness. One is an outer Reed–Solomon error correction code which corrects defective
ATSC-M/H
Golay codes for forward error correction 1950 – Richard Hamming publishes Hamming code paper, creates a new field of study Coding theory 1951 – Solomon
Timeline of information theory
Timeline_of_information_theory
achievable by concatenated codes. The bound states that there exists a family of q {\displaystyle q} -ary (concatenated, linear) codes with rate r {\displaystyle
Zyablov_bound
Type of data transmission method
targets Interleaved deltas Source Code Control System – Version control system for source code String-to-string correction problem Xdelta: open-source delta
Delta_encoding
Artificial production of human speech
process is speech recognition. Synthesized speech can be created by concatenating pieces of recorded speech that are stored in a database. Systems differ
Speech_synthesis
magnetic or other media subject to storage errors. Many archive formats contain extra error detection or correction information which can be used by the software
List_of_archive_formats
Computing) (February 26, 2025). "Hardware-efficient quantum error correction via concatenated bosonic qubits". Nature. 638 (8052): 927–935. arXiv:2409.13025
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
decoding, trellis shaping, and multilevel structure for high-rate parity-concatenated TCM". IEEE Transactions on Communications. 50 (1): 48–55. doi:10.1109/26
Iterative_Viterbi_decoding
Programming language with English-like syntax
ADD a, b TO c ON SIZE ERROR DISPLAY "Error" END-ADD ADD a TO b NOT SIZE ERROR DISPLAY "No error" ON SIZE ERROR DISPLAY "Error" The height of COBOL's
COBOL
Microcode in x86 Intel processors
to issue further error correction Control micro-operations (Cuops). In order to simplify restart, the Cuops originating from the error-causing macroinstruction
Intel_microcode
Unicode character block
there were three errors in Unicode 1.1: U+384E: 삤 in the Unicode Character Database, but 삣 in the Unicode 1.0 and ISO/IEC 10646-1:1993 code charts and per
Hangul_Syllables
Algorithms for calculating square roots
Since the computed error was not exact, this is not the actual answer, but becomes our new guess to use in the next round of correction. The process of updating
Square_root_algorithms
Second revision of the DVB-T standard
in "physical layer pipes" (PLPs), using OFDM modulation with concatenated channel coding and interleaving. The higher offered bit rate, with respect to
DVB-T2
Range of mainframe computers in the 1960s and 70s
extra bits being used for engineering purposes such as a Hamming code error-correction field, but these were never seen by programmers. The current incarnation
Burroughs_Large_Systems
Theorem in quantum information theory
Kitaev, A Yu (1997-12-31). "Quantum computations: algorithms and error correction". Russian Mathematical Surveys. 52 (6): 1191–1249. Bibcode:1997RuMaS
Solovay–Kitaev_theorem
Satellite radio service owned by SiriusXM
and error-free audio from a signal impaired by interference and fading, the receiver uses concatenated Reed-Solomon block coding and Forward Error Correction
Sirius_Satellite_Radio
Natural number
929: Tanakh B'yachad. The PDF417 barcode format uses a GF(929) error-correction code. 930 = 2 × 3 × 5 × 31. It is a pronic number. 931 = 72 × 19. It
900_(number)
Video encoding standard
codecs, such as Dolby Digital (AC-3) and Advanced Audio Coding (AAC) (mostly within the margin of error—and substantially superior in some cases, such as audience
MPEG-1
IEEE standard for broadband over power lines
error correction (FEC) scheme based on convolutional turbo code (CTC). The second option "Wavelet PHY" includes a mandatory FEC based on concatenated
IEEE_1901
International standards for dates and times
that restricts the supported date and time formats to reduce the chance of error and the complexity of software. The very simple specification is based on
ISO_8601
Application of computational algorithms, methods and programs to phylogenetic analyses
corrected for the possibility of back mutations at individual sites. This correction is done through the use of a substitution matrix such as that derived
Computational_phylogenetics
Basic unit of quantum information
{\displaystyle r} of the vector that represents the mixed state. Quantum error correction can be used to maintain the purity of qubits. Various kinds of physical
Qubit
Mainframe computer operating system
moved or copied to different physical disk drives. Disks can also be concatenated so that a single volume can be installed across several drives, as well
Burroughs_MCP
1 16-bit parallel error detection and correction three-state 40 SN74ALS616 74x617 1 16-bit parallel error detection and correction open-collector 40 SN74ALS617
List of 7400-series integrated circuits
List_of_7400-series_integrated_circuits
Quantum channel
efficiencies η {\displaystyle \eta } and η ′ {\displaystyle \eta '} can be concatenated. Such a concatenation gives a new channel of efficiency η {\displaystyle
Amplitude_damping_channel
Quantum analog of probabilistic automata
as an ergodic process, or more accurately, a mixing process that only concatenates transformations onto a state, but also smears the state over time. There
Quantum_finite_automaton
Computer science debate
was neither a true datagram network nor did it provide end-to-end error correction. Pouzin 1975"Arpanet ... provides only for basic services allowing
Protocol_Wars
CONCATENATED ERROR-CORRECTION-CODE
CONCATENATED ERROR-CORRECTION-CODE
CONCATENATED ERROR-CORRECTION-CODE
CONCATENATED ERROR-CORRECTION-CODE
CONCATENATED ERROR-CORRECTION-CODE
CONCATENATED ERROR-CORRECTION-CODE
CONCATENATED ERROR-CORRECTION-CODE
CONCATENATED ERROR-CORRECTION-CODE
CONCATENATED ERROR-CORRECTION-CODE