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 101011000 00100011
10011011 10110010
00100001 10100001
00011110 01111101
10001001 00010110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11010011 11010101 111011011 00111011 1
00011111 01111010 0
00100111 10111010 1
11001001 10011101 1
10111001 10110011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11110010 00000101 100100000 10001110 1
00100100 11010100 1
10100111 00101111 1
00101110 11010001 0
11111111 10101001 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:
01011000 00100011 0
10011011 10110010 1
00100001 10100001 1
00011110 01111101 0
10001001 00010110 0
01110101 01011011 0
1. The parity bits for the 16 columns is: 01110101 01011011
2. The parity bits for the 5 rows is: 01100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (1,0):
11010011 11010101 1
11011011 00111011 1
00011111 01111010 0
00100111 10111010 1
11001001 10011101 1
10111001 10110011 0
For figure 3, the bits that were flipped are (12,2) and (0,3):
11110010 00000101 1
00100000 10001110 1
00100100 11010100 1
10100111 00101111 1
00101110 11010001 0
11111111 10101001 0
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 0111010101011011
The answer was: 01100
The answer was: 0
The answer was: 1,0
The answer was: No