Error correction code: Difference between revisions

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Code-rate and the tradeoff between reliability and data rate: Incorrect word used, changed "rate" to "ratio".
Replaced word "ameliorates" with "alleviates" for ease of readability
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[[File:Interleaving1.png|right|400px|thumb|A short illustration of interleaving idea.]]
 
Interleaving is frequently used in digital communication and storage systems to improve the performance of forward error correcting codes. Many [[communication channel]]s are not memoryless: errors typically occur in [[burst error|burst]]s rather than independently. If the number of errors within a [[code word]] exceeds the error-correcting code's capability, it fails to recover the original code word. Interleaving amelioratesalleviates this problem by shuffling source symbols across several code words, thereby creating a more [[Uniform distribution (continuous)|uniform distribution]] of errors.<ref name="turbo-principles">{{cite book |author-first1=B. |author-last1=Vucetic |author-first2=J. |author-last2=Yuan |title=Turbo codes: principles and applications |publisher=[[Springer Verlag]] |isbn=978-0-7923-7868-6 |date=2000}}</ref> Therefore, interleaving is widely used for [[burst error-correcting code|burst error-correction]].
 
The analysis of modern iterated codes, like [[turbo code]]s and [[LDPC code]]s, typically assumes an independent distribution of errors.<ref>{{cite journal |author-first1=Michael |author-last1=Luby |author-link1=Michael Luby |author-first2=M. |author-last2=Mitzenmacher |author-first3=A. |author-last3=Shokrollahi |author-first4=D. |author-last4=Spielman |author-first5=V. |author-last5=Stemann |title=Practical Loss-Resilient Codes |journal=Proc. 29th Annual [[Association for Computing Machinery]] (ACM) Symposium on Theory of Computation |date=1997}}</ref> Systems using LDPC codes therefore typically employ additional interleaving across the symbols within a code word.<ref>{{Cite journal |title=Digital Video Broadcast (DVB); Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other satellite broadband applications (DVB-S2) |journal=En 302 307 |issue=V1.2.1 |publisher=[[ETSI]] |date=April 2009}}</ref>