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 101010000 10010010
11111010 01010011
11101101 10010011
10110110 11010111
00100100 10010100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011001 01110011 011011011 01100010 1
01000100 11101100 1
11111010 00000010 1
11000001 11011101 0
10111101 00100010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11111001 00011010 011000001 00111100 1
10110001 10000101 1
00101101 11101011 0
01110000 00011001 1
11010100 00010000 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:
01010000 10010010 1
11111010 01010011 0
11101101 10010011 0
10110110 11010111 1
00100100 10010100 1
11010101 00010001 1
1. The parity bits for the 16 columns is: 11010101 00010001
2. The parity bits for the 5 rows is: 10011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (16,4):
00011001 01110011 0
11011011 01100010 1
01000100 11101100 1
11111010 00000010 1
11000001 11011101 0
10111101 00100010 0
For figure 3, the bits that were flipped are (9,4) and (15,0):
11111001 00011010 0
11000001 00111100 1
10110001 10000101 1
00101101 11101011 0
01110000 00011001 1
11010100 00010000 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: 1101010100010001
The answer was: 10011
The answer was: 1
The answer was: 16,4
The answer was: No