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 100001001 00110111
10111111 11000110
00100111 11110110
10100100 01010000
01110100 00110101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11001100 11110011 001010010 01110100 1
10011110 11010011 0
11010000 01110010 1
00110011 10111010 1
11101011 10011100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01101111 11001000 010111011 10010100 1
01110101 11000110 0
10010011 01010111 1
01101000 00111010 1
01011011 11110011 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:
00001001 00110111 1
10111111 11000110 1
00100111 11110110 0
10100100 01010000 1
01110100 00110101 0
01000001 01100010 1
1. The parity bits for the 16 columns is: 01000001 01100010
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (4,5):
11001100 11110011 0
01010010 01110100 1
10011110 11010011 0
11010000 01110010 1
00110011 10111010 1
11101011 10011100 1
For figure 3, the bits that were flipped are (13,0) and (7,2):
01101111 11001000 0
10111011 10010100 1
01110101 11000110 0
10010011 01010111 1
01101000 00111010 1
01011011 11110011 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: 0100000101100010
The answer was: 11010
The answer was: 1
The answer was: 4,5
The answer was: No