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 111111011 01100100
01100011 00000101
11100100 01101000
11011101 10110100
10000010 01101011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11100110 01100010 010001001 00100010 0
00011100 01111110 1
00101111 01001100 0
01110100 10100101 0
00101000 11000111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10010011 00111111 011100010 10100100 0
01000111 01000111 0
01101111 10111100 1
10000101 01101001 1
11011100 00101001 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:
11111011 01100100 0
01100011 00000101 0
11100100 01101000 1
11011101 10110100 0
10000010 01101011 1
00100011 11010110 0
1. The parity bits for the 16 columns is: 00100011 11010110
2. The parity bits for the 5 rows is: 00101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,1):
11100110 01100010 0
10001001 00100010 0
00011100 01111110 1
00101111 01001100 0
01110100 10100101 0
00101000 11000111 1
For figure 3, the bit that was flipped is (10,1):
10010011 00111111 0
11100010 10100100 0
01000111 01000111 0
01101111 10111100 1
10000101 01101001 1
11011100 00101001 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: 0010001111010110
The answer was: 00101
The answer was: 0
The answer was: 11,1
The answer was: Yes