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 111101111 10110100
00110001 11011110
11010101 10100010
00011100 10111110
00001111 10000011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00010001 00011101 000111110 10001101 1
10101110 10001110 1
01011011 11100110 0
10111000 00011001 0
01100010 11100101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100111 11011110 111001100 11000110 0
11110101 00010100 1
10101111 01000101 0
10110110 10100010 0
01100111 10101011 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:
11101111 10110100 1
00110001 11011110 1
11010101 10100010 0
00011100 10111110 1
00001111 10000011 1
00011000 11110101 0
1. The parity bits for the 16 columns is: 00011000 11110101
2. The parity bits for the 5 rows is: 11011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (13,4):
00010001 00011101 0
00111110 10001101 1
10101110 10001110 1
01011011 11100110 0
10111000 00011001 0
01100010 11100101 0
For figure 3, the bits that were flipped are (2,2) and (9,3):
01100111 11011110 1
11001100 11000110 0
11110101 00010100 1
10101111 01000101 0
10110110 10100010 0
01100111 10101011 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: 0001100011110101
The answer was: 11011
The answer was: 0
The answer was: 13,4
The answer was: No