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 100110011 00100101
01110100 01000111
10001110 10001010
01111110 00100000
01111111 11100100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10110010 00000101 001000010 11111111 1
11001000 00010010 1
01010000 00100111 0
01100001 11101111 0
00001001 00100010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000110 00000000 110011101 11101000 0
01111000 00011100 1
11010100 00111010 0
00010110 11000000 0
11100001 10001110 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:
00110011 00100101 1
01110100 01000111 0
10001110 10001010 1
01111110 00100000 1
01111111 11100100 1
11001000 00101100 0
1. The parity bits for the 16 columns is: 11001000 00101100
2. The parity bits for the 5 rows is: 10111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,1):
10110010 00000101 0
01000010 11111111 1
11001000 00010010 1
01010000 00100111 0
01100001 11101111 0
00001001 00100010 0
For figure 3, the bits that were flipped are (1,1) and (8,4):
10000110 00000000 1
10011101 11101000 0
01111000 00011100 1
11010100 00111010 0
00010110 11000000 0
11100001 10001110 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: 1100100000101100
The answer was: 10111
The answer was: 0
The answer was: 14,1
The answer was: No