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 101101000 00001110
00100000 00100011
00001110 11100011
01001011 10001101
00110111 00011100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00110111 11101000 110110101 11011010 1
10101000 11101110 1
11111101 11111100 1
01111101 01011100 0
10101010 01111000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01010010 01110000 001011111 10011100 0
11010100 01110001 1
01010101 11110110 0
01111010 11101000 1
01110110 10000011 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:
01101000 00001110 0
00100000 00100011 0
00001110 11100011 0
01001011 10001101 0
00110111 00011100 0
00111010 01011111 0
1. The parity bits for the 16 columns is: 00111010 01011111
2. The parity bits for the 5 rows is: 00000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (13,1):
00110111 11101000 1
10110101 11011010 1
10101000 11101110 1
11111101 11111100 1
01111101 01011100 0
10101010 01111000 0
For figure 3, the bits that were flipped are (0,5) and (16,2):
01010010 01110000 0
01011111 10011100 0
11010100 01110001 1
01010101 11110110 0
01111010 11101000 1
01110110 10000011 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: 0011101001011111
The answer was: 00000
The answer was: 0
The answer was: 13,1
The answer was: No