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The error location is firstly detected.
These three bits give us the error location.
Now we have the error location, we could simply flip the bit corresponding to the error location and the error will be corrected.
000 indicating that there were no errors in transmission and the rest from 001 to 111 indicate the error location in our seven bit received codeword.
and also, the relation of syndromes to the error location numbers and to the magnitudes of the errors are given by the equation s i, w i = ∑ u i = 1 v i Y i, u i X i, u i w i, for 1 ≤ w i ≤ 2 t i. Open image in new window (2).
Thus, the elementary symmetric functions σ i, 1, σ i, 2, σ i, 3, ⋯, σ i, v i Open image in new window of the error location numbers X i, 1, X i, 2, X i, 3, ⋯, X i, v i Open image in new window are defined as the coefficients of the polynomials ( X − X i, 1 ) ( X − X i, 2 ) ⋯ ( X − X i, v i ) = X v i + σ i, 1 X v i − 1 + ⋯ + σ i, v i − 1 X + σ i, v i, Open image in new window .
Similar(53)
The received packets can be viewed as the coded packet corrupted (modulo- added) with packets having 1's in the error locations.
In this paper, we assume that the error locations are known at the decoder, as often presumed in error concealment literature, which can be done at transport level or based on syntax and watermarking [6].
From the received packets arranged row-wise in a matrix, we have to infer first which packet(s) is are) in error, and then, within this(these) packet(s), where the error locations are and their values.
That is the resultant error location considering the localization of that node only.
The selected elements give the correct error location numbers. .
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com