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 111010000 01111000
00001111 00101010
10111010 00000101
11110011 10111000
00010100 00111111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011100 10101010 100001100 10001111 1
10100100 11110110 1
01010010 00010110 1
00000111 10000111 1
11100001 01000010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011010 00111101 001101100 11011111 1
01011110 10111000 0
11011100 10101000 0
01001001 00001011 0
01111101 01111001 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:
11010000 01111000 1
00001111 00101010 1
10111010 00000101 1
11110011 10111000 0
00010100 00111111 0
10000010 11010000 1
1. The parity bits for the 16 columns is: 10000010 11010000
2. The parity bits for the 5 rows is: 11100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (16,3):
00011100 10101010 1
00001100 10001111 1
10100100 11110110 1
01010010 00010110 1
00000111 10000111 1
11100001 01000010 0
For figure 3, the bit that was flipped is (8,2):
11011010 00111101 0
01101100 11011111 1
01011110 10111000 0
11011100 10101000 0
01001001 00001011 0
01111101 01111001 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: 1000001011010000
The answer was: 11100
The answer was: 1
The answer was: 16,3
The answer was: Yes