Photo:1
Photo:2
Photo:3
Photo:4
Photo:1 Photo:2 Photo:3 Photo:4 |
| Formal definition | |
| 2>
Let X represent the space of signals that can be transmitted, and Y the space of signals received, during a block of time over the channel. Let
be the conditional distribution function of Y given X. Treating the channel as a known statistic system, pY | X(y | x) is an inherent fixed property of the communications channel (representing the nature of the noise in it). Then the joint distribution
of X and Y is completely determined by the channel and by the choice of
the marginal distribution of signals we choose to send over the channel. The joint distribution can be recovered by using the identity
Under these constraints, next maximize the amount of information, or the message, that one can communicate over the channel. The appropriate measure for this is the mutual information I(X;Y), and this maximum mutual information is called the channel capacity and is given by
[edit] Tags:Information,Communications Channel,Channel,Mutual Information, | |
| Noisy-channel coding theorem | |
| 2>
The noisy-channel coding theorem states that for any ε > 0 and for any rate R less than the channel capacity C, there is an encoding and decoding scheme that can be used to ensure that the probability of block error is less than ε for a sufficiently long code. Also, for any rate greater than the channel capacity, the probability of block error at the receiver goes to one as the block length goes to infinity.
[edit] Tags:Noisy-channel Coding Theorem,Receiver, | |
| Example application | |
| 2>
An application of the channel capacity concept to an additive white Gaussian noise (AWGN) channel with B Hz bandwidth and signal-to-noise ratio S/N is the Shannon–Hartley theorem:
C is measured in bits per second if the logarithm is taken in base 2, or nats per second if the natural logarithm is used, assuming B is in hertz; the signal and noise powers S and N are measured in watts or volts2, so the signal-to-noise ratio here is expressed as a power ratio, not in decibels (dB); since figures are often cited in dB, a conversion may be needed. For example, 30 dB is a power ratio of 1030 / 10 = 103 = 1000.
[edit] Tags:Additive White Gaussian Noise,Bandwidth,Signal-to-noise Ratio,Bits Per Second,Logarithm,Nats Per Second,Natural Logarithm,Hertz,Decibels,Shannon–hartley Theorem, | |
| Channel capacity in wireless communications | |
| 2>
This section[4] focuses on the single-antenna, point-to-point scenario. For channel capacity in systems with multiple antennas, see the article on MIMO.
[edit] Tags:Mimo, | |
| AWGN channel | |
| 3>
If the average received power is [W] and the noise power spectral density is N0 [W/Hz], the AWGN channel capacity is
[bits/Hz],
where is the received signal-to-noise ratio (SNR).
When the SNR is large (SNR >> 0 dB), the capacity is logarithmic in power and approximately linear in bandwidth. This is called the bandwidth-limited regime.
When the SNR is small (SNR << 0 dB), the capacity is linear in power but insensitive to bandwidth. This is called the power-limited regime.
The bandwidth-limited regime and power-limited regime are illustrated in the figure.
AWGN channel capacity with the power-limited regime and bandwidth-limited regime indicated. Here, .
[edit] Tags: | |
| Frequency-selective channel | |
| 3>
The capacity of the frequency-selective channel is given by so-called waterfilling power allocation,
where and is the gain of subchannel n, with λ chosen to meet the power constraint.
[edit] Tags:Frequency-selective, | |
| Slow-fading channel | |
| 3>
In a slow-fading channel, where the coherence time is greater than the latency requirement, there is no definite capacity as the maximum rate of reliable communications supported by the channel, log 2(1 + | h | 2SNR), depends on the random channel gain | h | 2. If the transmitter encodes data at rate R [bits/s/Hz], there is a certain probability that the decoding error probability cannot be made arbitrarily small,
,
in which case the system is said to be in outage. With a non-zero probability that the channel is in deep fade, the capacity of the slow-fading channel in strict sense is zero. However, it is possible to determine the largest value of R such that the outage probability pout is less than . This value is known as the -outage capacity.
[edit] Tags: | |
| Fast-fading channel | |
| 3>
In a fast-fading channel, where the latency requirement is greater than the coherence time and the codeword length spans many coherence periods, one can average over many independent channel fades by coding over a large number of coherence time intervals. Thus, it is possible to achieve a reliable rate of communication of [bits/s/Hz] and it is meaningful to speak of this value as the capacity of the fast-fading channel.
[edit] Tags: | |
| See also | |
| 2>
Bandwidth (computing)
Bandwidth (signal processing)
Bit rate
Code rate
Error exponent
Nyquist rate
Negentropy
Redundancy
Sender, Encoder, Decoder, Receiver
Shannon–Hartley theorem
Spectral efficiency
Throughput
[edit] Tags:Bandwidth (computing),Bandwidth (signal Processing),Bit Rate,Code Rate,Error Exponent,Nyquist Rate,Negentropy,Redundancy,Sender,Encoder,Decoder,Spectral Efficiency,Throughput, | |
| References | |
| 2>
^ Saleem Bhatti. "Channel capacity". Lecture notes for M.Sc. Data Communication Networks and Distributed Systems D51 -- Basic Communications and Networks. http://www.cs.ucl.ac.uk/staff/S.Bhatti/D51-notes/node31.html.
^ Jim Lesurf. "Signals look like noise!". Information and Measurement, 2nd ed.. http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/iandm/part8/page1.html.
^ Thomas M. Cover, Joy A. Thomas (2006), Elements of Information Theory, John Wiley & Sons, New York
^ David Tse, Pramod Viswanath (2005), Fundamentals of Wireless Communication, Cambridge University Press, UK
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2008)
Retrieved from "http://en.wikipedia.org/w/index.php?title=Channel_capacity&oldid=469967847"
Categories: Information theoryTelecommunication theoryTelevision terminologyHidden categories: Articles needing additional references from January 2008All articles needing additional references
Personal tools
Log in / create account
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
Actions
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact Wikipedia
Toolbox
What links here
Related changes
Upload file
Special pages
Permanent link
Cite this page
Print/export
Create a bookDownload as PDFPrintable version
Languages
Български
Deutsch
Ελληνικά
Español
فارسی
한국어
Italiano
Magyar
Nederlands
日本語
Polski
Русский
Українська
中文
This page was last modified on 6 January 2012 at 20:57.
Text is available under the Creative Commons Attribution-ShareAlike License;
additional terms may apply.
See Terms of use for details.
Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.Contact us
Privacy policy
About Wikipedia
Disclaimers
Mobile view
if ( window.isMSIE55 ) fixalpha();
if ( window.mediaWiki ) {
mw.loader.load(["mediawiki.user", "mediawiki.util", "mediawiki.page.ready", "mediawiki.legacy.wikibits", "mediawiki.legacy.ajax", "mediawiki.legacy.mwsuggest", "ext.gadget.wmfFR2011Style", "ext.vector.collapsibleNav", "ext.vector.collapsibleTabs", "ext.vector.editWarning", "ext.vector.simpleSearch", "ext.UserBuckets", "ext.articleFeedback.startup", "ext.articleFeedbackv5.startup", "ext.markAsHelpful"]);
}
if ( window.mediaWiki ) {
mw.user.options.set({"ccmeonemails":0,"cols":80,"date":"default","diffonly":0,"disablemail":0,"disablesuggest":0,"editfont":"default","editondblclick":0,"editsection":1,"editsectiononrightclick":0,"enotifminoredits":0,"enotifrevealaddr":0,"enotifusertalkpages":1,"enotifwatchlistpages":0,"extendwatchlist":0,"externaldiff":0,"externaleditor":0,"fancysig":0,"forceeditsummary":0,"gender":"unknown","hideminor":0,"hidepatrolled":0,"highlightbroken":1,"imagesize":2,"justify":0,"math":1,"minordefault":0,"newpageshidepatrolled":0,"nocache":0,"noconvertlink":0,"norollbackdiff":0,"numberheadings":0,"previewonfirst":0,"previewontop":1,"quickbar":5,"rcdays":7,"rclimit":50,"rememberpassword":0,"rows":25,"searchlimit":20,"showhiddencats":false,"showjumplinks":1,"shownumberswatching":1,"showtoc":1,"showtoolbar":1,"skin":"vector","stubthreshold":0,"thumbsize":4,"underline":2,"uselivepreview":0,"usenewrc":0,"watchcreations":1,"watchdefault":0,"watchdeletion":0,"watchlistdays":3,"watchlisthideanons":0,
"watchlisthidebots":0,"watchlisthideliu":0,"watchlisthideminor":0,"watchlisthideown":0,"watchlisthidepatrolled":0,"watchmoves":0,"wllimit":250,"flaggedrevssimpleui":1,"flaggedrevsstable":0,"flaggedrevseditdiffs":true,"flaggedrevsviewdiffs":false,"vector-simplesearch":1,"useeditwarning":1,"vector-collapsiblenav":1,"usebetatoolbar":1,"usebetatoolbar-cgd":1,"wikilove-enabled":1,"variant":"en","language":"en","searchNs0":true,"searchNs1":false,"searchNs2":false,"searchNs3":false,"searchNs4":false,"searchNs5":false,"searchNs6":false,"searchNs7":false,"searchNs8":false,"searchNs9":false,"searchNs10":false,"searchNs11":false,"searchNs12":false,"searchNs13":false,"searchNs14":false,"searchNs15":false,"searchNs100":false,"searchNs101":false,"searchNs108":false,"searchNs109":false,"gadget-wmfFR2011Style":1});;mw.user.tokens.set({"editToken":"+\\","watchToken":false});;mw.loader.state({"user.options":"ready","user.tokens":"ready"});
/* cache key: enwiki:resourceloader:filter:minify-js:4:b41a86ec4e0fe8329bc3ce917e792339 */
}
Tags:Information Theory,Reliable Sources,Challenged,Categories,Telecommunication Theory,Television Terminology, | |
zote monety |