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 110001011 00101011
11001101 11001101
01000111 00111001
00110101 01000010
01000010 11100110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011011 00110011 001110101 00100010 1
01010001 01011011 1
01101010 11110110 0
01101100 01111011 0
00101001 11000111 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11010010 10000111 000110001 11100100 1
00001101 11010111 1
11000100 10110101 0
10010100 10000111 0
10111110 10000010 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:
10001011 00101011 0
11001101 11001101 0
01000111 00111001 0
00110101 01000010 0
01000010 11100110 1
01110110 01111011 1
1. The parity bits for the 16 columns is: 01110110 01111011
2. The parity bits for the 5 rows is: 00001
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (3,2):
00011011 00110011 0
01110101 00100010 1
01010001 01011011 1
01101010 11110110 0
01101100 01111011 0
00101001 11000111 0
For figure 3, the bit that was flipped is (13,4):
11010010 10000111 0
00110001 11100100 1
00001101 11010111 1
11000100 10110101 0
10010100 10000111 0
10111110 10000010 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: 0111011001111011
The answer was: 00001
The answer was: 1
The answer was: 3,2
The answer was: Yes