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 100100110 01011111
10110001 10011100
10101001 01111011
10010010 10110110
10110100 00110111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010011 11000001 110001010 11001000 0
11001010 01101101 0
11111010 00111010 0
11110100 00001011 0
11011101 01110101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00001001 10100110 001111101 00011000 1
00110100 01100010 1
01000011 11011001 0
00110010 11100010 1
00110000 11110111 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:
00100110 01011111 1
10110001 10011100 0
10101001 01111011 0
10010010 10110110 0
10110100 00110111 1
00011000 00111001 0
1. The parity bits for the 16 columns is: 00011000 00111001
2. The parity bits for the 5 rows is: 10001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (10,2):
10010011 11000001 1
10001010 11001000 0
11001010 01101101 0
11111010 00111010 0
11110100 00001011 0
11011101 01110101 1
For figure 3, the bits that were flipped are (7,2) and (11,1):
00001001 10100110 0
01111101 00011000 1
00110100 01100010 1
01000011 11011001 0
00110010 11100010 1
00110000 11110111 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: 0001100000111001
The answer was: 10001
The answer was: 0
The answer was: 10,2
The answer was: No