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 100011111 00101011
01000111 00100110
00100011 00010100
01111011 01101100
11100101 00001011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001010 00011010 010010101 01001101 1
10110100 01110010 0
11011011 01110111 0
11101000 11101101 0
00011000 10111111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01010010 00001101 000000010 10001101 0
11010011 01011010 0
10110100 11100000 1
00010110 00110110 1
10100001 10001100 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:
00011111 00101011 1
01000111 00100110 1
00100011 00010100 1
01111011 01101100 0
11100101 00001011 0
11100101 01111110 1
1. The parity bits for the 16 columns is: 11100101 01111110
2. The parity bits for the 5 rows is: 11100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (1,1):
01001010 00011010 0
10010101 01001101 1
10110100 01110010 0
11011011 01110111 0
11101000 11101101 0
00011000 10111111 1
For figure 3, the bits that were flipped are (0,1) and (8,2):
01010010 00001101 0
00000010 10001101 0
11010011 01011010 0
10110100 11100000 1
00010110 00110110 1
10100001 10001100 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: 1110010101111110
The answer was: 11100
The answer was: 1
The answer was: 1,1
The answer was: No