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 100010001 01011011
01110101 01100010
00111101 01000011
10100110 01110110
00101101 01110000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00010101 11011110 011001001 10010011 0
10101000 00111000 0
01111101 11010110 1
00000111 01011111 1
00001010 11111100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00000001 00110110 110100101 10111111 1
10100111 10010111 1
11001011 00100000 0
11101000 01001100 0
00101000 01110110 1
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:
00010001 01011011 1
01110101 01100010 0
00111101 01000011 0
10100110 01110110 1
00101101 01110000 1
11010010 01111100 1
1. The parity bits for the 16 columns is: 11010010 01111100
2. The parity bits for the 5 rows is: 10011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (5,0):
00010101 11011110 0
11001001 10010011 0
10101000 00111000 0
01111101 11010110 1
00000111 01011111 1
00001010 11111100 0
For figure 3, the bits that were flipped are (13,2) and (4,4):
00000001 00110110 1
10100101 10111111 1
10100111 10010111 1
11001011 00100000 0
11101000 01001100 0
00101000 01110110 1
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: 1101001001111100
The answer was: 10011
The answer was: 1
The answer was: 5,0
The answer was: No