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 111001000 10011100
00111001 11001100
10100010 11100011
11000110 11011000
10101111 11101011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01010100 01000000 000011001 10111100 0
00100110 01001000 1
00110001 11011001 0
10110110 00010110 1
11101100 01111111 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110110 10100010 100101011 10010111 1
00001011 00001101 0
10010010 01000110 1
11111001 00000010 1
00111101 01110101 0
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:
11001000 10011100 1
00111001 11001100 0
10100010 11100011 0
11000110 11011000 0
10101111 11101011 0
00111010 10000000 1
1. The parity bits for the 16 columns is: 00111010 10000000
2. The parity bits for the 5 rows is: 10000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,4):
01010100 01000000 0
00011001 10111100 0
00100110 01001000 1
00110001 11011001 0
10110110 00010110 1
11101100 01111111 0
For figure 3, the bits that were flipped are (12,0) and (15,3):
01110110 10100010 1
00101011 10010111 1
00001011 00001101 0
10010010 01000110 1
11111001 00000010 1
00111101 01110101 0
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: 0011101010000000
The answer was: 10000
The answer was: 1
The answer was: 13,4
The answer was: No