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 101000001 11110000
01100100 10011101
10011011 00011001
11110001 10100000
00011111 01101110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001000 10001001 101000110 10000110 0
00011100 01100000 1
00010111 10010000 0
00110000 10010001 0
11111101 01101110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00100111 00011101 111001011 10101111 1
10100001 00011011 1
01100111 10001110 1
10111010 01110100 0
10110000 01110011 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:
01000001 11110000 0
01100100 10011101 0
10011011 00011001 0
11110001 10100000 1
00011111 01101110 0
01010000 10111010 1
1. The parity bits for the 16 columns is: 01010000 10111010
2. The parity bits for the 5 rows is: 00010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (4,4):
10001000 10001001 1
01000110 10000110 0
00011100 01100000 1
00010111 10010000 0
00110000 10010001 0
11111101 01101110 0
For figure 3, the bits that were flipped are (2,0) and (10,4):
00100111 00011101 1
11001011 10101111 1
10100001 00011011 1
01100111 10001110 1
10111010 01110100 0
10110000 01110011 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: 0101000010111010
The answer was: 00010
The answer was: 1
The answer was: 4,4
The answer was: No