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 110110101 01100010
10001001 01010001
01000001 00111110
00000111 01011000
00101001 01110110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101110 10111110 010010011 01101101 1
11100000 01011110 1
01100101 11011011 0
01011000 00111101 0
01110000 01101011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10110010 00110110 010110101 11001111 1
10110000 01001101 0
01100000 00000010 1
01110011 01011011 0
10100100 11101001 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:
10110101 01100010 0
10001001 01010001 0
01000001 00111110 1
00000111 01011000 0
00101001 01110110 0
01010011 00100011 1
1. The parity bits for the 16 columns is: 01010011 00100011
2. The parity bits for the 5 rows is: 00100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (3,2):
00101110 10111110 0
10010011 01101101 1
11100000 01011110 1
01100101 11011011 0
01011000 00111101 0
01110000 01101011 0
For figure 3, the bit that was flipped is (13,2):
10110010 00110110 0
10110101 11001111 1
10110000 01001101 0
01100000 00000010 1
01110011 01011011 0
10100100 11101001 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0101001100100011
The answer was: 00100
The answer was: 1
The answer was: 3,2
The answer was: Yes