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 111010101 11101010
11101010 01000000
00110100 01110100
01001111 11011101
01100000 00110000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11010000 11011010 000001010 00100011 1
01000111 10001100 0
11111100 10111000 0
10010100 01111100 0
11110100 10110001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10111100 00100101 000011001 10101010 0
11100011 10101011 0
10101000 01101001 1
00001010 01001011 0
11101100 01000110 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:
11010101 11101010 0
11101010 01000000 0
00110100 01110100 1
01001111 11011101 1
01100000 00110000 0
00100100 00110011 0
1. The parity bits for the 16 columns is: 00100100 00110011
2. The parity bits for the 5 rows is: 00110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (7,2):
11010000 11011010 0
00001010 00100011 1
01000111 10001100 0
11111100 10111000 0
10010100 01111100 0
11110100 10110001 1
For figure 3, the bits that were flipped are (4,1) and (9,5):
10111100 00100101 0
00011001 10101010 0
11100011 10101011 0
10101000 01101001 1
00001010 01001011 0
11101100 01000110 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: 0010010000110011
The answer was: 00110
The answer was: 0
The answer was: 7,2
The answer was: No