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 110100110 00101000
00111000 01110010
00001000 01001010
01011101 11000101
01011011 00000101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01010001 01111101 101100000 00100110 1
00001001 11010000 0
10110111 00110011 0
10100000 00111110 1
00001111 10000110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011110 10011000 100000111 10001010 1
00001101 00110100 1
11010110 10111011 1
00111001 10011011 1
01111011 10000110 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:
10100110 00101000 0
00111000 01110010 1
00001000 01001010 0
01011101 11000101 1
01011011 00000101 1
10010000 11010000 1
1. The parity bits for the 16 columns is: 10010000 11010000
2. The parity bits for the 5 rows is: 01011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (2,2):
01010001 01111101 1
01100000 00100110 1
00001001 11010000 0
10110111 00110011 0
10100000 00111110 1
00001111 10000110 1
For figure 3, the bits that were flipped are (1,1) and (8,2):
11011110 10011000 1
00000111 10001010 1
00001101 00110100 1
11010110 10111011 1
00111001 10011011 1
01111011 10000110 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: 1001000011010000
The answer was: 01011
The answer was: 1
The answer was: 2,2
The answer was: No