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 101101000 10111011
01111100 11101111
01100001 11110010
00011101 10010100
00000000 01011000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00111100 00000001 101100001 00101110 1
11001010 10111000 1
00010110 11111010 1
00010011 10011111 1
10010010 11110010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011011 00000111 001110000 00001011 0
10101111 01100011 0
00001000 01010111 0
01100111 10000100 1
01100011 10110100 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:
01101000 10111011 1
01111100 11101111 0
01100001 11110010 0
00011101 10010100 1
00000000 01011000 1
01101000 01101010 1
1. The parity bits for the 16 columns is: 01101000 01101010
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 (16,2):
00111100 00000001 1
01100001 00101110 1
11001010 10111000 1
00010110 11111010 1
00010011 10011111 1
10010010 11110010 0
For figure 3, the bits that were flipped are (4,0) and (12,5):
11011011 00000111 0
01110000 00001011 0
10101111 01100011 0
00001000 01010111 0
01100111 10000100 1
01100011 10110100 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: 0110100001101010
The answer was: 10011
The answer was: 1
The answer was: 16,2
The answer was: No