Shannon–Hartley theorem
E645105
The Shannon–Hartley theorem is a fundamental result in information theory that quantifies the maximum error-free data transmission rate over a communication channel with a given bandwidth and signal-to-noise ratio.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf | channel capacity theorem ⓘ |
| appliesTo |
band-limited AWGN channel
ⓘ
communication channel ⓘ continuous-time channels ⓘ |
| assumes |
Gaussian noise distribution
ⓘ
additive white Gaussian noise ⓘ band-limited channel ⓘ ideal coding and modulation ⓘ linear time-invariant channel ⓘ perfect error-correcting codes exist at capacity ⓘ |
| bandwidthUnit | hertz ⓘ |
| category | Theorems in information theory ⓘ |
| characterizes | fundamental limit of reliable communication ⓘ |
| contrastsWith | practical system performance below capacity ⓘ |
| describes |
channel capacity
ⓘ
maximum error-free data transmission rate ⓘ |
| establishes | upper bound on reliable communication rate ⓘ |
| expressesAs | C = B log2(1 + S/N) ⓘ |
| field | information theory NERFINISHED ⓘ |
| givesFormulaFor | channel capacity in bits per second ⓘ |
| implies | error-free transmission is bounded by channel capacity ⓘ |
| influences |
coding theory
ⓘ
modulation scheme selection ⓘ spectrum efficiency analysis ⓘ |
| namedAfter |
Claude Shannon
NERFINISHED
ⓘ
Ralph Hartley NERFINISHED ⓘ |
| relatedTo |
Hartley’s law
NERFINISHED
ⓘ
Shannon’s noisy-channel coding theorem NERFINISHED ⓘ |
| relatesQuantity |
bandwidth
ⓘ
channel capacity ⓘ signal-to-noise ratio ⓘ |
| showsThat |
capacity growth with SNR is logarithmic
ⓘ
capacity increases with bandwidth ⓘ capacity increases with signal-to-noise ratio ⓘ |
| unitOfCapacity | bits per second ⓘ |
| usedFor |
estimating maximum data rate of a link
ⓘ
link budget analysis ⓘ |
| usedIn |
data transmission system design
ⓘ
digital communications ⓘ modem design ⓘ wireless communications ⓘ |
| usesSymbol |
B for bandwidth
ⓘ
C for channel capacity ⓘ N for noise power ⓘ S for signal power ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.