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 101000111 00011000
00101111 11101010
01111111 10011010
10111101 00001101
00001100 10001000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00000001 00011110 101001110 11000001 1
01100011 11110011 0
01110111 01001011 1
01111000 01101011 1
00100011 00001100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10101101 00101111 010011101 11011001 1
00001000 01110111 1
00111001 01101111 0
10000010 11100111 1
10000011 11001001 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:
01000111 00011000 0
00101111 11101010 0
01111111 10011010 1
10111101 00001101 1
00001100 10001000 0
10100110 11101101 0
1. The parity bits for the 16 columns is: 10100110 11101101
2. The parity bits for the 5 rows is: 00110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,3):
00000001 00011110 1
01001110 11000001 1
01100011 11110011 0
01110111 01001011 1
01111000 01101011 1
00100011 00001100 1
For figure 3, the bits that were flipped are (9,4) and (8,1):
10101101 00101111 0
10011101 11011001 1
00001000 01110111 1
00111001 01101111 0
10000010 11100111 1
10000011 11001001 1
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 1010011011101101
The answer was: 00110
The answer was: 0
The answer was: 16,3
The answer was: No