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. 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. A burst of length ℓ {displaystyle ell } Say a codeword C {displaystyle C} is transmitted, and it is received as Y = C + E . {displaystyle Y=C+E.} Then, the error vector E {displaystyle E} is called a burst of length ℓ {displaystyle ell } if the nonzero components of E {displaystyle E} are confined to ℓ {displaystyle ell } consecutive components. For example, E = ( 0 1000011 0 ) {displaystyle E=(0{ extbf {1000011}}0)} is a burst of length ℓ = 7. {displaystyle ell =7.}