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Burst error-correcting code
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Burst error-correcting code : ウィキペディア英語版
Burst error-correcting code
In coding theory, burst error-correcting codes employ methods of correcting burst errors, which are errors that occur in many consecutive bits rather than occurring in bits independently of each other.
Many codes have been designed to correct random errors. Sometimes, however, channels may introduce errors which are localized in a short interval. Such errors occur in a burst (called burst errors) because they occur in many consecutive bits. Examples of burst errors can be found extensively in storage mediums. These errors may be due to physical damage such as scratch on a disc or a stroke of lightning in case of wireless channels. They are not independent; they tend to be spatially concentrated. If one bit has an error, it is likely that the adjacent bits could also be corrupted. The methods used to correct random errors are inefficient to correct burst errors.
==Definitions==

A burst of length \textstyle l〔Coding Bounds for Multiple Phased-Burst Correction and Single Burst Correction Codes〕
Say a codeword \textstyle C is transmitted, and it is received as \textstyle Y = C + E. Then, the error vector \textstyle E is called a burst of length \textstyle l if the nonzero components of \textstyle E are confined to \textstyle l consecutive components. For example, \textstyle E = (0\textbf0) is a burst of length \textstyle l = 7.
Although this definition is sufficient to describe what a burst error is, the majority of the tools developed for burst error correction rely on cyclic codes. This motivates our next definition.
A cyclic burst of length \textstyle l
An error vector \textstyle E is called a cyclic burst error of length \textstyle l if its nonzero components are confined to \textstyle l cyclically consecutive components. For example, the previously considered error vector \textstyle E = (010000110), is a cyclic burst of length \textstyle l = 5, since we consider the error starting at position \textstyle 6 and ending at position \textstyle 1. Notice the indices are \textstyle 0-based, that is, the first element is at position \textstyle 0.
For the remainder of this article, we will use the term burst to refer to a cyclic burst, unless noted otherwise.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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