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 101001011 11000101
00000001 10011101
01010110 01100011
01011000 10011101
00010110 11111001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01010101 01101100 001111100 00011100 1
01101111 01100010 1
10010110 10100110 0
10001110 00111100 0
11011110 10001000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00100101 00010000 001010001 01101110 0
01111111 01010100 0
00100110 11011111 1
10010010 10011100 1
10111111 01100001 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:
01001011 11000101 0
00000001 10011101 0
01010110 01100011 0
01011000 10011101 0
00010110 11111001 1
01010010 01011111 1
1. The parity bits for the 16 columns is: 01010010 01011111
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 (0,1):
01010101 01101100 0
01111100 00011100 1
01101111 01100010 1
10010110 10100110 0
10001110 00111100 0
11011110 10001000 0
For figure 3, the bit that was flipped is (12,3):
00100101 00010000 0
01010001 01101110 0
01111111 01010100 0
00100110 11011111 1
10010010 10011100 1
10111111 01100001 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0101001001011111
The answer was: 00001
The answer was: 1
The answer was: 0,1
The answer was: Yes