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 110110100 00111001
01100110 11001000
00101110 01101011
01111100 01101011
10000110 01001101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110111 10011101 101000000 11010111 1
00101100 01001101 1
01000101 11011011 1
11110100 11101011 0
10101010 00110111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10010001 11100111 010111011 10100011 1
01000001 11111111 0
11011011 01010110 0
10010110 10101110 1
00100110 01110011 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:
10110100 00111001 0
01100110 11001000 1
00101110 01101011 1
01111100 01101011 0
10000110 01001101 1
00000110 10111100 1
1. The parity bits for the 16 columns is: 00000110 10111100
2. The parity bits for the 5 rows is: 01101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (16,4):
01110111 10011101 1
01000000 11010111 1
00101100 01001101 1
01000101 11011011 1
11110100 11101011 0
10101010 00110111 1
For figure 3, the bits that were flipped are (11,0) and (10,1):
10010001 11100111 0
10111011 10100011 1
01000001 11111111 0
11011011 01010110 0
10010110 10101110 1
00100110 01110011 0
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: 0000011010111100
The answer was: 01101
The answer was: 1
The answer was: 16,4
The answer was: No