Coding theory: Difference between revisions

Revision as of 04:24, 31 July 2023

Revision as of 09:45, 3 August 2023

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|date=2002

|page=18

|publisher=John Wiley & Sons

|section=2.4.4 Types of Coding

|quote=There are four types of coding|isbn=9780471808725

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==Cryptographic coding==

{{main|Cryptography}}

[[Cryptography]] or cryptographic coding is the practice and study of techniques for [[secure communication]] in the presence of third parties (called [[adversary (cryptography)|adversaries]]).<ref name="rivest90">{{cite book|first=Ronald L.|last=Rivest|author-link=Ron Rivest|editor=J. Van Leeuwen|title=Handbook of Theoretical Computer Science|chapter=Cryptology|volume=1|publisher=Elsevier|year=1990}}</ref> More generally, it is about constructing and analyzing [[communications protocol|protocol]]s that block adversaries;<ref name="modern-crypto">{{Cite book|first1=Mihir|last1=Bellare|first2=Phillip|last2=Rogaway|title=Introduction to Modern Cryptography|chapter=Introduction|page=10|date=21 September 2005}}</ref> various aspects in [[information security]] such as data [[confidentiality]], [[data integrity]], [[authentication]], and [[non-repudiation]]<ref name="hac">{{cite book |first1=A. J. |last1=Menezes |first2=P. C. |last2=van Oorschot |first3=S. A. |last3=Vanstone |url=https://archive.org/details/handbookofapplie0000mene |title=Handbook of Applied Cryptography |isbn=978-0-8493-8523-0 |year=1997 |publisher=Taylor & Francis |url-access=registration }}</ref> are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of [[mathematics]], [[computer science]], and [[electrical engineering]]. Applications of cryptography include [[automated teller machine|ATM cards]], [[password|computer passwords]], and [[electronic commerce]].

Cryptography prior to the modern age was effectively synonymous with ''[[encryption]]'', the conversion of information from a readable state to apparent [[nonsense]]. The originator of an encrypted message shared the decoding technique needed to recover the original information only with intended recipients, thereby precluding unwanted persons from doing the same. Since [[World War&nbsp;I]] and the advent of the [[computer]], the methods used to carry out cryptology have become increasingly complex and its application more widespread.

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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 webjournal |url= http://tools.ietf.org/html/rfc793 |title= RFC793 |workjournal= RFCsRFCS|publisher= [[Internet Engineering Task Force]] (IETF) |date= September 1981}}

===Group testing===