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 111001111 00111011
11011101 11000111
11011101 11100010
00010010 01101011
11110110 10000000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110011 10010011 000111101 10101000 0
01001100 11010111 1
01101110 01001110 1
01101001 10000001 0
10010101 00100011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110101 10010001 110100100 11010100 1
00001011 10010011 1
10111100 00110000 1
00001001 01010011 0
01101111 10010101 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:
11001111 00111011 1
11011101 11000111 1
11011101 11100010 0
00010010 01101011 1
11110110 10000000 1
00101011 11110101 0
1. The parity bits for the 16 columns is: 00101011 11110101
2. The parity bits for the 5 rows is: 11011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,5):
11110011 10010011 0
00111101 10101000 0
01001100 11010111 1
01101110 01001110 1
01101001 10000001 0
10010101 00100011 0
For figure 3, the bit that was flipped is (10,0):
01110101 10010001 1
10100100 11010100 1
00001011 10010011 1
10111100 00110000 1
00001001 01010011 0
01101111 10010101 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: 0010101111110101
The answer was: 11011
The answer was: 0
The answer was: 3,5
The answer was: Yes