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 110100100 11110111
01100000 00000100
01000111 01010110
10111001 01000011
00010100 10010001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10000101 11011111 000110101 01000011 1
10100100 00000001 0
10010100 01011110 1
10100101 01100111 1
00100001 10100100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10110000 10100100 010101001 01100110 0
00100000 11101000 1
01101110 01011001 1
00001101 00100000 1
01011010 01010111 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:
10100100 11110111 0
01100000 00000100 1
01000111 01010110 0
10111001 01000011 0
00010100 10010001 1
00101110 01110111 0
1. The parity bits for the 16 columns is: 00101110 01110111
2. The parity bits for the 5 rows is: 01001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (5,3):
10000101 11011111 0
00110101 01000011 1
10100100 00000001 0
10010100 01011110 1
10100101 01100111 1
00100001 10100100 1
For figure 3, the bit that was flipped is (13,4):
10110000 10100100 0
10101001 01100110 0
00100000 11101000 1
01101110 01011001 1
00001101 00100000 1
01011010 01010111 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0010111001110111
The answer was: 01001
The answer was: 0
The answer was: 5,3
The answer was: Yes