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 11110111
10100111 00100110
00011010 01010110
01100011 11111010
11101101 01110001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01011110 00000001 000000110 00100011 1
11010010 00110101 0
00011011 01001011 0
11100110 11100001 1
01110011 10111101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011111 00101101 001100011 10110011 1
01000000 11000001 0
11111100 11100001 0
01011011 10011001 0
01011001 00100011 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:
01011000 11110111 0
10100111 00100110 0
00011010 01010110 1
01100011 11111010 0
11101101 01110001 0
01101011 00001100 1
1. The parity bits for the 16 columns is: 01101011 00001100
2. The parity bits for the 5 rows is: 00100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (5,5):
01011110 00000001 0
00000110 00100011 1
11010010 00110101 0
00011011 01001011 0
11100110 11100001 1
01110011 10111101 0
For figure 3, the bits that were flipped are (13,4) and (6,0):
11011111 00101101 0
01100011 10110011 1
01000000 11000001 0
11111100 11100001 0
01011011 10011001 0
01011001 00100011 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: 0110101100001100
The answer was: 00100
The answer was: 1
The answer was: 5,5
The answer was: No