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 110100110 10101100
10111111 00100101
00010011 00000110
01010110 00001011
11000100 11000100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01111100 01010100 010011001 11011110 1
10100100 11110010 0
11011101 10011111 0
00101100 10101110 0
10110000 11001001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000011 00100101 000111111 00101010 1
00100111 01101111 0
10001011 11111100 1
00110100 01001011 1
11100100 11010111 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:
10100110 10101100 0
10111111 00100101 0
00010011 00000110 1
01010110 00001011 1
11000100 11000100 0
10011000 01000000 0
1. The parity bits for the 16 columns is: 10011000 01000000
2. The parity bits for the 5 rows is: 00110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (8,1):
01111100 01010100 0
10011001 11011110 1
10100100 11110010 0
11011101 10011111 0
00101100 10101110 0
10110000 11001001 1
For figure 3, the bits that were flipped are (0,3) and (1,5):
10000011 00100101 0
00111111 00101010 1
00100111 01101111 0
10001011 11111100 1
00110100 01001011 1
11100100 11010111 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: 1001100001000000
The answer was: 00110
The answer was: 0
The answer was: 8,1
The answer was: No