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 101010001 11000000
01100010 01010101
11110011 11100101
11100001 10010000
00100001 01011010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00000001 10010110 101010101 11111010 0
10011010 11110010 1
10101011 01011000 1
01011001 10111101 0
00111101 01111011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00111011 01000001 010011101 00000000 1
10111010 00111000 0
00011001 01010101 1
11010111 01100011 0
11100010 01001111 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:
01010001 11000000 1
01100010 01010101 1
11110011 11100101 1
11100001 10010000 0
00100001 01011010 0
00000000 10111010 1
1. The parity bits for the 16 columns is: 00000000 10111010
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 (7,3):
00000001 10010110 1
01010101 11111010 0
10011010 11110010 1
10101011 01011000 1
01011001 10111101 0
00111101 01111011 1
For figure 3, the bits that were flipped are (2,0) and (3,5):
00111011 01000001 0
10011101 00000000 1
10111010 00111000 0
00011001 01010101 1
11010111 01100011 0
11100010 01001111 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: 0000000010111010
The answer was: 11100
The answer was: 1
The answer was: 7,3
The answer was: No