Editing Coding theory (section)

==Other applications of coding theory==
{{misleading|date=August 2012}}

Another concern of coding theory is designing codes that help [[synchronization]]. A code may be designed so that a [[Phase (waves)|phase shift]] can be easily detected and corrected and that multiple signals can be sent on the same channel.{{Citation needed|date=July 2008}}

Another application of codes, used in some mobile phone systems, is [[code-division multiple access]] (CDMA). Each phone is assigned a code sequence that is approximately uncorrelated with the codes of other phones.{{Citation needed|date=July 2008}} When transmitting, the code word is used to modulate the data bits representing the voice message. At the receiver, a demodulation process is performed to recover the data. The properties of this class of codes allow many users (with different codes) to use the same radio channel at the same time. To the receiver, the signals of other users will appear to the demodulator only as a low-level noise.{{Citation needed|date=July 2008}}

Another general class of codes are the [[automatic repeat-request]] (ARQ) codes. In these codes the sender adds redundancy to each message for error checking, usually by adding check bits. If the check bits are not consistent with the rest of the message when it arrives, the receiver will ask the sender to retransmit the message. All but the simplest [[wide area network]] protocols use ARQ. Common protocols include [[Synchronous Data Link Control|SDLC]] (IBM), [[Transmission Control Protocol|TCP]] (Internet), [[X.25]] (International) and many others. There is an extensive field of research on this topic because of the problem of matching a rejected packet against a new packet. Is it a new one or is it a retransmission? Typically numbering schemes are used, as in TCP.{{cite journal |url= http://tools.ietf.org/html/rfc793 |title= RFC793 |journal= RFCS|publisher= [[Internet Engineering Task Force]] (IETF) |date= September 1981}}

===Group testing===
[[Group testing]] uses codes in a different way. Consider a large group of items in which a very few are different in a particular way (e.g., defective products or infected test subjects). The idea of group testing is to determine which items are "different" by using as few tests as possible. The origin of the problem has its roots in the [[Second World War]] when the [[United States Army Air Forces]] needed to test its soldiers for [[syphilis]].<ref>{{cite journal |last1=Dorfman |first1=Robert |title=The detection of defective members of large populations |journal=Annals of Mathematical Statistics |date=1943 |volume=14 |issue=4 |pages=436–440|doi=10.1214/aoms/1177731363 |doi-access=free }}</ref>

===Analog coding===
Information is encoded analogously in the [[neural network]]s of [[brain]]s, in [[analog signal processing]], and [[analog electronics]]. Aspects of analog coding include analog error correction,<ref>{{cite journal | title = Analog Error-Correcting Codes Based on Chaotic Dynamical Systems | citeseerx = 10.1.1.30.4093 | first1 = Brian | last1 = Chen | first2 = Gregory W. | last2 = Wornell | journal = IEEE Transactions on Communications | volume = 46 | issue = 7 | date = July 1998 | pages = 881–890 | doi = 10.1109/26.701312 | url = http://allegro.mit.edu/dspg/publications/Journals/pdf/98Chen.pdf | access-date = 2013-06-30 | archive-url = http://webarchive.loc.gov/all/20010927045421/http://allegro.mit.edu/dspg/publications/journals/pdf/98chen.pdf | archive-date = 2001-09-27 | url-status = dead }}</ref>
analog data compression<ref>
{{cite conference | title = On Analog Signature Analysis | citeseerx=10.1.1.142.5853 | first1 = Franc | last1 = Novak | first2 = Bojan | last2 = Hvala | first3 = Sandi | last3 = Klavžar | book-title = Proceedings of the conference on Design, automation and test in Europe | year = 1999 | isbn = 1-58113-121-6 }}
</ref> and analog encryption.<ref>
{{cite journal |author1=Shujun Li |author2=Chengqing Li |author3=Kwok-Tung Lo |author4=Guanrong Chen |title=Cryptanalyzing an Encryption Scheme Based on Blind Source Separation |journal=IEEE Transactions on Circuits and Systems I |volume=55 |issue=4 |pages=1055–63 |date=April 2008 |doi=10.1109/TCSI.2008.916540 |arxiv=cs/0608024 |s2cid=2224947 |url=http://epubs.surrey.ac.uk/532452/1/IEEETCASI2008.pdf }}
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