Suppose the codeword length is 8. Answer the following questions, with proper justification. in. (10 points) Give an example of undetectable error burst of length 6; ii. (10 points) Give an example of undetectable 6-bit error;

Burst Error

The term burst error means that two or more bits in the data unit have changed from 0 to  1 or vice-versa. Note that burst error doesn’t necessary means that error occurs in  consecutive bits. The length of the burst error is measured from the first corrupted bit to  the last corrupted bit. Some bits in between may not be corrupted.

Example of undetectable error burst of length 6

Say a codeword $ C $ is transmitted, and it is received as $ Y = C + E $. Then, the error vector $ E $ is called a burst of length $ l $ if the number of nonzero components of $ E $ is confined to $ l $ consecutive components. For example, $ E = (0\textbf{1000011}0) $ is a burst of length $ 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.

For example, the burst description of the error pattern $ E = (010000110) $ is $ D = (1000011,1) $. Notice that such description is not unique, because $ D' = (11001,6) $ is describing the same burst error. In general, if the number of nonzero components in $ E $ is $ w $, then $ E $ will have $ w $ different burst descriptions (each starting at a different nonzero entry of $ E $).