EXAMPLE 2 Error Correction

For practice, we will do another example. Consider the message 0111. Proceeding as before, we place 0 in region I and 1s in regions II, III, and IV. For regions V, VI, VII, we assign 0 or 1 so that the total number of 1s in each circle is even (see Figure 17.5). Then the message 0111 is encoded as 0111001. If this code word is received as, say, 0111011 (error in the sixth position), the diagram for the received word is shown in Figure 17.6. Then circle has an odd number of 1s, and circles and have an even number. If the received message has only one error, then the error must be in circle but not circles and . This tells us that the entry is region VI is incorrect. So, the error can be corrected.