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Limit on data transfer rate
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise
Noisy-channel_coding_theorem
Theorem that tells the maximum rate at which information can be transmitted
the noisy-channel coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise. The theorem establishes
Shannon–Hartley_theorem
Establishes the limits to possible data compression
be made arbitrarily small, by making n larger. Channel coding Error exponent Noisy-channel coding theorem Shen, A. and Uspensky, V.A. and Vereshchagin,
Shannon's source coding theorem
Shannon's_source_coding_theorem
Information-theoretical limit on transmission rate in a communication channel
over a communication channel. Following the terms of the noisy-channel coding theorem, the channel capacity of a given channel is the highest information
Channel_capacity
Scheme for controlling errors in data over noisy communication channels
improving the received effective signal-to-noise ratio. The noisy-channel coding theorem of Claude Shannon can be used to compute the maximum achievable
Error_correction_code
Common communications channel model
applied to varied communication channels such as telephone lines or disk drive storage. The noisy-channel coding theorem applies to BSCp, saying that information
Binary_symmetric_channel
given by the noisy-channel coding theorem; the practical result of the Shannon–Hartley law for the channel capacity of a Gaussian channel; and of course
History_of_information_theory
Study of the properties of codes and their fitness
given by the noisy-channel coding theorem; the practical result of the Shannon–Hartley law for the channel capacity of a Gaussian channel; and of course
Coding_theory
Average uncertainty in variable's states
perfectly noiseless channel. Shannon strengthened this result considerably for noisy channels in his noisy-channel coding theorem. Entropy in information
Entropy_(information_theory)
be wrong. Noisy channel coding theorem See Deppe 2007 and Hill 1995. Berlekamp 1964. Deppe 2007. Berlekamp, Elwyn R. (1964). Block coding with noiseless
Error-correcting codes with feedback
Error-correcting_codes_with_feedback
Scientific study of digital information
channel noise. Shannon's main result, the noisy-channel coding theorem, showed that, in the limit of many channel uses, the rate of information that is asymptotically
Information_theory
Topic in mathematics
{1}{N}}|\operatorname {set} (H_{N})|.} Cramér's theorem (large deviations) Noisy-channel coding theorem Shannon's source coding theorem Cover & Thomas (1991), p. 51. Hawkins
Asymptotic equipartition property
Asymptotic_equipartition_property
Maximum rate of a quantum channel
the direct coding theorem and the converse theorem. The direct coding theorem demonstrates that the quantum mutual information of the channel is an achievable
Entanglement-assisted classical capacity
Entanglement-assisted_classical_capacity
Type of set in information theory
properties of typical sequences, efficient coding schemes like Shannon's source coding theorem and channel coding theorem are developed, enabling near-optimal
Typical_set
Model of noisy digital information transfer and storage.
the capacity 1 − P e {\displaystyle 1-P_{e}} . However, by the noisy-channel coding theorem, the capacity of 1 − P e {\displaystyle 1-P_{e}} can be obtained
Binary_erasure_channel
Theory about lossy data compression
user. We also know from Shannon's channel coding theorem that if the source entropy is H bits/symbol, and the channel capacity is C (where C < H {\displaystyle
Rate–distortion_theory
American mathematician (1916–2001)
codes with feedback List of pioneers in computer science Models of communication n-gram Noisy channel coding theorem Nyquist–Shannon sampling theorem
Claude_Shannon
Basic noise model used in information theory
and about 98% of the time inside the 3σ circle. Ground bounce Noisy-channel coding theorem Gaussian process McClaning, Kevin, Radio Receiver Design, Noble
Additive_white_Gaussian_noise
Information-theoretic measure
information theory, the Kraft–McMillan theorem establishes that any directly decodable coding scheme for coding a message to identify one value x i {\displaystyle
Cross-entropy
Topics referred to by the same term
biodiversity index Noisy-channel coding theorem, sometimes called Shannon Limit, the theoretical limit to capacity of a communication channel Shannan (disambiguation)
Shannon
1948 scholarly article by Claude Shannon
work is known for introducing the concepts of channel capacity as well as the noisy channel coding theorem. Shannon's article laid out the basic elements
A Mathematical Theory of Communication
A_Mathematical_Theory_of_Communication
Information held in the state of a quantum system
fundamental theorems of information theory: noiseless channel coding theorem and noisy channel coding theorem. He also showed that error correcting codes could
Quantum_information
expected to receive as much information as predicted by the noisy channel coding theorem. Real-world receivers include: For modulated radio waves, a radio
Receiver_(information_theory)
Time density of the average information in a stochastic process
equipartition property Rate–distortion theory Shannon's source coding theorem Channel capacity Noisy-channel coding theorem Shannon–Hartley theorem v t e
Entropy_rate
Measure of dependence between two variables
beginning of the article. In terms of a communication channel in which the output Y {\displaystyle Y} is a noisy version of the input X {\displaystyle X} , these
Mutual_information
Amount of useful work accomplished by a computer
over a communications channel. By the noisy-channel coding theorem, the channel capacity of a given channel is the limiting information rate (in units
Computer_performance
Kullback–Leibler divergence lossless compression negentropy noisy-channel coding theorem (Shannon's theorem) principle of maximum entropy quantum information science
Index of information theory articles
Index_of_information_theory_articles
Slepian–Wolf theorem gives a theoretical bound for the lossless coding rate for distributed coding of the two sources. The bound for the lossless coding rates
Slepian–Wolf_coding
Information theory
{\displaystyle x\in \mathrm {supp} \,X.} Then, using the disintegration theorem: P ( M | X = x ) = lim U ∋ x P ( M ∩ { X ∈ U } ) P ( { X ∈ U } ) and P
Conditional mutual information
Conditional_mutual_information
Foundational object in quantum communication theory
Schumacher, Benjamin (1 June 1998). "Information transmission through a noisy quantum channel". Physical Review A. 57 (6): 4153–4175. arXiv:quant-ph/9702049.
Quantum_channel
Problem in information theory and communication
for Wyner-Ziv coding and related source-coding problems. Similar to the previous lossless coding framework based on Slepian–Wolf theorem, efforts have
Distributed_source_coding
Filters used in signal processing that are optimal in some sense
likelihood Detection theory Multiple comparisons problem Channel capacity Noisy-channel coding theorem Spectral density estimation Least mean squares (LMS)
Matched_filter
Notion in information theory
equipartition property Rate–distortion theory Shannon's source coding theorem Channel capacity Noisy-channel coding theorem Shannon–Hartley theorem v t e
Limiting density of discrete points
Limiting_density_of_discrete_points
Measure of information in probability and information theory
2000). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. New York: Dover Publications. ISBN 0-486-41147-8
Joint_entropy
Measure of relative information in probability theory
equipartition property Rate–distortion theory Shannon's source coding theorem Channel capacity Noisy-channel coding theorem Shannon–Hartley theorem v t e
Conditional_entropy
Process in quantum computing
for a sender and receiver to simulate a noiseless qubit channel given a noisy qubit channel whose noise conforms to a particular error model. Much of
Quantum_error_correction
Concept in information theory
represents the amount of discrete information that can be transmitted over a channel that admits a continuous space of values. For the direct analogue of discrete
Differential_entropy
Topics referred to by the same term
to: Shannon's source coding theorem, which establishes the theoretical limits to lossless data compression Shannon–Hartley theorem, which establishes the
Shannon's_law
List of definitions of terms and concepts used in electrical engineering and electronics
path. noisy-channel coding theorem A theorem that establishes the limits of the error-free data transmission in a noisy communication channel nominal
Glossary of electrical and electronics engineering
Glossary_of_electrical_and_electronics_engineering
System of rules to convert information into another form or representation
is the reverse process, converting code symbols back into a form that the recipient understands. One role of coding is to enable communication in places
Code
Algorithms to decode messages
over a noisy channel, such as a binary symmetric channel. C ⊂ F 2 n {\displaystyle C\subset \mathbb {F} _{2}^{n}} is considered a binary code with the
Decoding_methods
Overview of computer engineering topics
Hamming code Hamming(7,4) Convolutional code Forward error correction Noisy-channel coding theorem Modulation Signal-to-noise ratio Linear code Noise (electronics)
Computer engineering compendium
Computer_engineering_compendium
Theorem in quantum computing
theory. The theorem is named after Bryan Eastin and Emanuel Knill, who published it in 2009. Since quantum computers are inherently noisy, quantum error
Eastin–Knill_theorem
American telecommunications company
legitimacy of the technology, due to its perceived violation of the noisy-channel coding theorem's “Shannon limit”. In May 2013, Rearden LLC sought an experimentation
Artemis_Networks
Family of error-correcting codes that encode data in blocks
Channel capacity Shannon–Hartley theorem Noisy channel List decoding Sphere packing Christian Schlegel; Lance Pérez (2004). Trellis and turbo coding.
Block_code
Quantum computing algorithm
distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant quantum computers.
Magic_state_distillation
Highest rate quantum information can be sent through a noisy quantum channel
a noisy quantum channel from a sender to a receiver. It is also equal to the highest rate at which entanglement can be generated over the channel, and
Quantum_capacity
Cryptography based on quantum mechanical phenomena
York, introduced the concept of quantum conjugate coding. His seminal paper titled "Conjugate Coding" was rejected by the IEEE Information Theory Society
Quantum_cryptography
State-dependent measures that converge to the mutual information
equipartition property Rate–distortion theory Shannon's source coding theorem Channel capacity Noisy-channel coding theorem Shannon–Hartley theorem v t e
State-dependent_information
In coding theory, list decoding is an alternative to unique decoding of error-correcting codes for large error rates. The notion was proposed by Elias
List_decoding
Method in quantum communication
{X}}_{s+c}|X_{c}\right\}.} The sender transmits all of her qubits over the noisy quantum channel. The receiver then possesses the transmitted qubits and his half
Entanglement-assisted stabilizer formalism
Entanglement-assisted_stabilizer_formalism
decoding. Data to be transmitted over a noisy channel may first be encoded using an SCCC. Upon reception, the coding may be used to remove any errors introduced
Serial concatenated convolutional codes
Serial_concatenated_convolutional_codes
Term in quantum information theory
rate achievable by a coding scheme for classical information transmission, which can be defined as follows. Definition. (Coding scheme) A ( n , m , δ
Classical_capacity
Class of error-correcting 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
Linear_code
Measurement of a quantum system which minimally disturbs it
S2CID 35809757. T. Ogawa; H. Nagaoka (1999). "Strong Converse to the Quantum Channel Coding Theorem". IEEE Trans. Inf. Theory. 45 (7): 2486–2489. arXiv:quant-ph/9808063
Weak_measurement
Message encoded with more bits than needed
redundant. Minimum redundancy coding Huffman encoding Data compression Hartley function Negentropy Source coding theorem Overcompleteness Here it is assumed
Redundancy (information theory)
Redundancy_(information_theory)
Process of "purifying" entangled quantum states
Entanglement distillation can overcome the degenerative influence of noisy quantum channels by transforming previously shared, less-entangled pairs into a smaller
Entanglement_distillation
Error-correcting code
and correction when transmitting messages over very noisy or unreliable channels. In 1971, the code was used to transmit photos of Mars back to Earth from
Hadamard_code
polarization scheme on three orthogonal bases and its ability to tolerate a noisier channel. DPS protocol (2002) is a simple and efficient quantum key distribution
List of quantum key distribution protocols
List_of_quantum_key_distribution_protocols
Computer hardware technology that uses quantum mechanics
light because the classical bits must travel through normal channels. Superdense coding is the complementary protocol: using one shared e-bit and sending
Quantum_computing
In coding theory, generalized minimum-distance (GMD) decoding provides an efficient algorithm for decoding concatenated codes, which is based on using
Generalized minimum-distance decoding
Generalized_minimum-distance_decoding
Experimental technology level
Noisy intermediate-scale quantum (NISQ) computing is characterized by quantum processors containing up to 1,000 qubits which are not advanced enough yet
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
Type of error-correcting codes
practically (due to Noisy Channel Coding Theory issues), quasi optimal tradeoffs can be achieved theoretically. Prior to Folded Reed–Solomon codes being devised
Folded_Reed–Solomon_code
Mathematical statistics distance measure
information theory, the Kraft–McMillan theorem establishes that any directly decodable coding scheme for coding a message to identify one value x i {\displaystyle
Kullback–Leibler_divergence
American quantum physicist
questioned whether the classical capacity of a noisy quantum channel might be increased by entangled codings, a result eventually established in the positive
Christopher_A._Fuchs
Computational benchmark
decoherence and noise. The threshold theorem states that a noisy quantum computer can use quantum error-correcting codes to simulate a noiseless quantum computer
Quantum_supremacy
Codes with the property that slight modifications of messages are difficult to make
several interesting real-world settings, such as data transmitted over a noisy channel, or adversarial tampering of data stored in the memory of a physical
Non-malleable_code
Quantum information paradigm
lossy and noisy environment. Many quantum information applications, such as quantum teleportation, quantum error correction, and superdense coding, rely on
Quantum_illumination
Physical phenomenon
no-cloning theorem is maintained as the information is recreated from the entangled state and not copied during teleportation. The quantum channel is the
Quantum_teleportation
Open-source framework for quantum computers
Cirq is an open-source framework for noisy intermediate scale quantum (NISQ) computers. Cirq was developed by the Google AI Quantum Team, and the public
Cirq
System that converts an analog signal into a digital signal
one voltage interval is assigned in between two consecutive code levels. Example: Coding scheme as in figure 1 Full scale measurement range = 0 to 1 volt
Analog-to-digital_converter
Projected date when quantum computers could break modern encryption
found more in academic and standards fields, especially around Mosca's theorem, a back-of-the-envelope test that asks a blunt question: if you add up
Quantum_Threat
Topological quantum error correcting code
be fault tolerant, which can be achieved by magic state distillation on noisy magic states. A measurement based scheme for quantum computation based upon
Surface_code
correcting code can transversely implement a universal gate set. Since quantum computers are inherently noisy, quantum error correcting codes are used to
Glossary_of_quantum_computing
Metric for a quantum computer's capabilities
speed, and reliability. rQOPS =[Q][f] Noisy intermediate-scale quantum era Quantum error correction Threshold theorem Finke, Doug; Shaw, David (21 Sep 2023)
RQOPS
Computer programming for quantum computers
value 0 The computation process is executed using a provided simulator. Noisy environments can be simulated using parameters of the simulator. A language
Quantum_programming
Quantum algorithm for integer factorization
theorem guarantees that the continued fractions algorithm will recover j / r {\displaystyle j/r} from k / 2 2 n {\displaystyle k/2^{2{n}}} : Theorem—If
Shor's_algorithm
Applications of machine learning to quantum physics
complex quantum systems brings with it a growing need to turn large and noisy data sets into meaningful information. This is a problem that has already
Machine_learning_in_physics
Quantum computing applied to natural language processing
classical data on a quantum computer. Thus, they are not applicable to the noisy intermediate-scale quantum (NISQ) computers available today. The algorithm
Quantum natural language processing
Quantum_natural_language_processing
Algorithm in mathematics
the identification of coding regions in prokaryotic DNA. GLIMMER uses Interpolated Markov Models (IMMs) to identify the coding regions and distinguish
Baum–Welch_algorithm
Search problem in quantum mechanics
Mendes, Leandro; Hsieh, Min-Hsiu (2025-04-15). "Unconditional advantage of noisy qudit quantum circuits over biased threshold circuits in constant depth"
Hidden linear function problem
Hidden_linear_function_problem
Technique for the generative modeling of a continuous probability distribution
textual language into a pictorial language". Then, as in noisy-channel model, we use Bayes theorem to get p ( x | y ) ∝ p ( y | x ) p ( x ) {\displaystyle
Diffusion_model
Quantum cryptographic method
discrete-variable protocol for quantum key distribution that permits tolerating a noisier channel than the BB84 protocol." (2011, Abruzzo). SSP produces a higher rate
Six-state_protocol
Type of feedforward neural network
subset of their most important inputs and become nearly invariant to the noisy inputs. L1 with L2 regularization can be combined; this is called elastic
Convolutional_neural_network
Mathematical modelling alogorithm
analogy between the problem of constructing models for noisy data and signal passing through the channel with noise. This made possible to lay the foundations
Group_method_of_data_handling
rediscover the no-cloning theorem of James L. Park. Charles Bennett and Gilles Brassard employ Wiesner's conjugate coding for distribution of cryptographic
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Subfield of quantum cryptography
distribution and typically assumed pre-shared entanglement or conjugate coding techniques; research on quantum message authentication and digital signatures
Quantum_authentication
Quantum algorithm
algorithms between quantum and classical computers. It is an example of a noisy intermediate-scale quantum (NISQ) algorithm. The objective of the VQE is
Variational quantum eigensolver
Variational_quantum_eigensolver
Quantum benchmarking protocol
quantum computer did generate those samples, then the quantum computer is too noisy and thus has no chance of performing beyond-classical computations. Since
Cross-entropy_benchmarking
Open-source software development kit
effect of measurement errors), aiming to return higher-quality outcomes from noisy quantum hardware. IBM Quantum Compute Service supports multiple execution
Qiskit
Networks connecting quantum processors
theorem. As a result, other types of error correction must be introduced such as the Shor code or one of a number of more general and efficient codes
Quantum_network
Statistical procedure of testing by group
called noisy group testing, and deals with a big assumption of the original problem: that testing is error-free. A group-testing problem is called noisy when
Group_testing
Computer network not fully connected by cables
Shannon's theorem can describe the maximum data rate of any single wireless link, which relates to the bandwidth in hertz and to the noise on the channel. One
Wireless_network
Method for assessing quantum computer hardware capabilities
Cory, David; Laflamme, Raymond (2007). "Symmetrized characterization of noisy quantum processes". Science. 317 (1095–9203): 1893–6. arXiv:0707.0685. Bibcode:2007Sci
Randomized_benchmarking
Artificial neural network
Neural Network (BCPNN) is an artificial neural network inspired by Bayes' theorem, which regards neural computation and processing as probabilistic inference
BCPNN
Interdisciplinary research area
preparation and measurement. VQAs are considered promising candidates for noisy intermediate-scale quantum computers. Variational quantum circuits (or parameterized
Quantum_machine_learning
Cascade of electronic components
things, including the method of detection, the signal coding method, the bandwidth of the RF channel, and whether or not digital processing is involved.
RF_chain
Process of removing noise from a signal
surrounding pixels; the defining characteristic is that the value of a noisy pixel bears no relation to the color of surrounding pixels. When viewed
Noise_reduction
Metric for a quantum computer's capabilities
bits are more valuable as a performance measure than a larger number of noisy, error-prone qubits. Generally, the larger the quantum volume, the more
Quantum_volume
NOISY CHANNEL-CODING-THEOREM
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