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 110001101 01101110
01010100 00001110
00000111 10110000
00101111 00100101
10011111 01100010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00111000 01110010 101010110 11001011 0
00001111 01101011 1
00111010 11001000 1
10101001 00011111 1
11110000 00000101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00010101 11110100 101010011 00001011 1
11110101 01001000 1
01011011 11001110 0
00001001 01010000 0
11100001 00011001 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:
10001101 01101110 1
01010100 00001110 0
00000111 10110000 0
00101111 00100101 0
10011111 01100010 1
01101110 10010111 0
1. The parity bits for the 16 columns is: 01101110 10010111
2. The parity bits for the 5 rows is: 10001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (6,1):
00111000 01110010 1
01010110 11001011 0
00001111 01101011 1
00111010 11001000 1
10101001 00011111 1
11110000 00000101 0
For figure 3, the bits that were flipped are (10,0) and (11,2):
00010101 11110100 1
01010011 00001011 1
11110101 01001000 1
01011011 11001110 0
00001001 01010000 0
11100001 00011001 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: 0110111010010111
The answer was: 10001
The answer was: 0
The answer was: 6,1
The answer was: No