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 100010010 00111100
00111011 01100110
01101100 11001010
00111010 01111001
01000001 11110111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00000010 10100100 110101111 11001010 0
11111001 00100000 1
01100001 11011011 1
00010010 01101101 1
00110111 11111000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11110100 01110010 001000000 01110010 1
01001111 11011101 0
11101111 01011110 0
00010001 10111100 1
01001101 00111111 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:
00010010 00111100 0
00111011 01100110 1
01101100 11001010 0
00111010 01111001 1
01000001 11110111 1
00111110 00011110 1
1. The parity bits for the 16 columns is: 00111110 00011110
2. The parity bits for the 5 rows is: 01011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (3,0):
00000010 10100100 1
10101111 11001010 0
11111001 00100000 1
01100001 11011011 1
00010010 01101101 1
00110111 11111000 0
For figure 3, the bits that were flipped are (1,2) and (4,0):
11110100 01110010 0
01000000 01110010 1
01001111 11011101 0
11101111 01011110 0
00010001 10111100 1
01001101 00111111 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: 0011111000011110
The answer was: 01011
The answer was: 1
The answer was: 3,0
The answer was: No