channel coding theorem
Shannon showed that an error-correcting code always exists that will reduce the probability of error below any predetermined level. He did not, however, show how to construct such a code (this remains the central problem of coding theory), although he did show that randomly chosen codes are as good as any others, provided they are extremely long.
Among Shannon's results for specific channels, the most celebrated is that for a power-limited continuous-amplitude channel subject to white Gaussian noise. If the signal power is limited to PS and the noise power is PN, the capacity of such a channel is C = ½ν log2(1 + PS/PN) bit/s
If it is a discrete-time channel, ν is the number of epochs per second; if it is a continuous-time channel, ν is the minimum number of samples per second necessary to acquire all the information from the channel. In the latter case, if ν is to be finite, the channel must be band-limited; if W is its bandwidth (in Hz), then, by Nyquist's criterion, C = W log2(1 + PS/PN) bit/s
This is sometimes called the Shannon–Hartley law, and is often applied, erroneously, in circumstances less restricted than those described. This and other expressions for the capacity of specific channels should not be confused with the channel coding theorem, which states only that there is a finite capacity (which may be zero) and that it can be attained without error.
See also Shannon's model, source coding theorem.
"channel coding theorem." A Dictionary of Computing. . Encyclopedia.com. (December 10, 2018). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/channel-coding-theorem
"channel coding theorem." A Dictionary of Computing. . Retrieved December 10, 2018 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/channel-coding-theorem
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.