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 111011010 11010010
11011001 10111010
10001010 01111101
00110001 00001011
01110011 01010001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00111001 10100101 000111010 00101001 1
01000010 11010101 1
01011111 00000100 0
10110101 10110010 1
10101011 11100111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01101100 00100101 111100110 10101110 0
00110001 11001001 0
01000000 01110111 1
10111001 00011000 1
01000010 01101101 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:
11011010 11010010 1
11011001 10111010 0
10001010 01111101 1
00110001 00001011 0
01110011 01010001 0
11001011 01001111 0
1. The parity bits for the 16 columns is: 11001011 01001111
2. The parity bits for the 5 rows is: 10100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (12,3):
00111001 10100101 0
00111010 00101001 1
01000010 11010101 1
01011111 00000100 0
10110101 10110010 1
10101011 11100111 1
For figure 3, the bit that was flipped is (9,2):
01101100 00100101 1
11100110 10101110 0
00110001 11001001 0
01000000 01110111 1
10111001 00011000 1
01000010 01101101 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: 1100101101001111
The answer was: 10100
The answer was: 0
The answer was: 12,3
The answer was: Yes