Error Detection and Correction: Two Dimensional Parity
Suppose that a packet’s payload consists of 10 eight-bit values (e.g., representing ten ASCII-encoded characters) shown below. (Here, we have arranged the ten eight-bit values as five sixteen-bit values):
Figure 100111011 00010001
11001001 00110001
00110110 01011100
11111111 01010011
00110111 00000110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101100 11000111 011111000 01100111 1
01000100 10010000 0
00100100 11110010 1
01100001 11011100 0
11010101 00010110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110011 01001010 011110100 10101100 1
01101100 01000010 0
00000110 01100001 1
01101111 11010010 0
10000011 00010111 0
Question List
1. For figure 1, compute the two-dimensional parity bits for the 16 columns. Combine the bits into one string
2. For figure 1, compute the two-dimensional parity bits for the 5 rows (starting from the top). Combine the bits into one string
3. For figure 1, compute the parity bit for the parity bit row from question 1. Assume that the result should be even.
4. For figure 2, indicate the row and column with the flipped bit (format as: x,y), assuming the top-left bit is 0,0
5. For figure 3, is it possible to detect and correct the bit flips? Yes or No
Solution
The full solution for figure 1 is shown below:
00111011 00010001 1
11001001 00110001 1
00110110 01011100 0
11111111 01010011 0
00110111 00000110 1
00001100 00101001 1
1. The parity bits for the 16 columns is: 00001100 00101001
2. The parity bits for the 5 rows is: 11001
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (12,1):
00101100 11000111 0
11111000 01100111 1
01000100 10010000 0
00100100 11110010 1
01100001 11011100 0
11010101 00010110 0
For figure 3, the bit that was flipped is (7,5):
01110011 01001010 0
11110100 10101100 1
01101100 01000010 0
00000110 01100001 1
01101111 11010010 0
10000011 00010111 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0000110000101001
The answer was: 11001
The answer was: 1
The answer was: 12,1
The answer was: Yes