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 110100001 01011000
11100000 01111001
11000111 11110101
11101001 00111100
10100100 01101110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001100 11111010 101011111 10000101 0
01101000 10111001 0
00111011 10110100 1
00000110 10110001 0
10000010 11000011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01111000 01011111 001111001 10001101 1
00000110 01101011 1
01011000 10100000 1
11000000 01001011 0
10011011 01010010 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:
10100001 01011000 0
11100000 01111001 0
11000111 11110101 1
11101001 00111100 1
10100100 01101110 0
11001011 10000110 0
1. The parity bits for the 16 columns is: 11001011 10000110
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 (5,1):
10001100 11111010 1
01011111 10000101 0
01101000 10111001 0
00111011 10110100 1
00000110 10110001 0
10000010 11000011 0
For figure 3, the bit that was flipped is (5,5):
01111000 01011111 0
01111001 10001101 1
00000110 01101011 1
01011000 10100000 1
11000000 01001011 0
10011011 01010010 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 1100101110000110
The answer was: 00110
The answer was: 0
The answer was: 5,1
The answer was: Yes