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 110101011 10100000
11011100 00011111
10011000 01011001
11011010 10011100
10111110 11111011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001110 10001001 100010010 11100000 1
00010011 00011000 0
10101101 10101110 0
01100110 01000000 1
10000100 11011111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000101 01000100 010100100 11101110 1
01100000 01011000 0
00101100 00011011 1
11000111 01110011 0
11001010 10011010 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:
10101011 10100000 1
11011100 00011111 0
10011000 01011001 1
11011010 10011100 1
10111110 11111011 1
10001011 10000001 0
1. The parity bits for the 16 columns is: 10001011 10000001
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 (9,2):
01001110 10001001 1
00010010 11100000 1
00010011 00011000 0
10101101 10101110 0
01100110 01000000 1
10000100 11011111 1
For figure 3, the bit that was flipped is (2,2):
11000101 01000100 0
10100100 11101110 1
01100000 01011000 0
00101100 00011011 1
11000111 01110011 0
11001010 10011010 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: 1000101110000001
The answer was: 10111
The answer was: 0
The answer was: 9,2
The answer was: Yes