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 110001011 01011110
00010100 01100100
00100110 11001100
11100110 11001010
00101100 11000110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11010001 11110111 101010110 01000011 1
10011001 11111100 1
11100100 11001111 0
00000011 01110011 1
11101001 11110100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011111 01001101 011111001 00100011 1
11010010 01000001 0
11011010 11011100 1
11001110 11001001 1
11100010 01111010 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:
10001011 01011110 1
00010100 01100100 1
00100110 11001100 1
11100110 11001010 1
00101100 11000110 1
01110011 11111010 1
1. The parity bits for the 16 columns is: 01110011 11111010
2. The parity bits for the 5 rows is: 11111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (3,2):
11010001 11110111 1
01010110 01000011 1
10011001 11111100 1
11100100 11001111 0
00000011 01110011 1
11101001 11110100 0
For figure 3, the bits that were flipped are (9,0) and (6,3):
11011111 01001101 0
11111001 00100011 1
11010010 01000001 0
11011010 11011100 1
11001110 11001001 1
11100010 01111010 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: 0111001111111010
The answer was: 11111
The answer was: 1
The answer was: 3,2
The answer was: No