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 111101001 11110011
10010111 11100101
11000000 01000010
01110011 11111001
10011110 00000000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11000110 00001010 110000111 01010100 1
01001110 11011110 0
10111001 00111110 0
01000001 01111001 1
11110111 11010111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11111011 01110110 011110100 00001000 0
00100011 11001010 1
11101110 11011000 0
11100101 01001001 1
00100111 00110101 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:
11101001 11110011 1
10010111 11100101 0
11000000 01000010 0
01110011 11111001 1
10011110 00000000 1
01010011 10101101 1
1. The parity bits for the 16 columns is: 01010011 10101101
2. The parity bits for the 5 rows is: 10011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (11,0):
11000110 00001010 1
10000111 01010100 1
01001110 11011110 0
10111001 00111110 0
01000001 01111001 1
11110111 11010111 1
For figure 3, the bit that was flipped is (11,4):
11111011 01110110 0
11110100 00001000 0
00100011 11001010 1
11101110 11011000 0
11100101 01001001 1
00100111 00110101 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: 0101001110101101
The answer was: 10011
The answer was: 1
The answer was: 11,0
The answer was: Yes