Error Detection Codes and Correction Codes(1)
An error: An incorrect value in one or more bits.
Single error: An incorrect value in only one bit.
Multiple error: One or more bits are incorrect.
Errors are introduced by hardware failures, external interference (noise), or other unwanted events.
Error detection/correction code: Information is encoded in such a way that a particular class of errors can be detected and/or corrected.
Let I and J be n-bit binary information words
- w(I): the number of 1’s in I (weight)
- d(I, J): the number of bit positions in which I and J differ (distance)
Example: I = (01101100) and J = (11000100)
- w(I) = 4 and w(J) = 3
- d(I, J) = 3.