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 101100010 11111011
11011000 01111110
10110100 01101001
00000000 00001100
01000000 11011101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00100001 00011011 001100000 01100111 1
11110000 01010110 0
00100111 01000111 1
00000111 11001010 1
10010001 10100011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01101111 01011100 110011000 00011010 0
00000111 10101111 0
00010010 10100111 1
01111010 01111011 1
10011000 00111111 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:
01100010 11111011 0
11011000 01111110 0
10110100 01101001 0
00000000 00001100 0
01000000 11011101 1
01001110 00111101 1
1. The parity bits for the 16 columns is: 01001110 00111101
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 (13,3):
00100001 00011011 0
01100000 01100111 1
11110000 01010110 0
00100111 01000111 1
00000111 11001010 1
10010001 10100011 1
For figure 3, the bits that were flipped are (14,0) and (12,2):
01101111 01011100 1
10011000 00011010 0
00000111 10101111 0
00010010 10100111 1
01111010 01111011 1
10011000 00111111 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: 0100111000111101
The answer was: 00001
The answer was: 1
The answer was: 13,3
The answer was: No