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 110000111 11001001
10100100 10000011
11101010 01111001
01100001 10000010
10000111 01010101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01010001 00001001 110101001 00000010 1
10111110 00011011 0
11100101 10011000 1
10000001 01000000 1
00100010 11000000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110001 11101000 010101111 10110100 1
01101110 01111100 0
10110011 11101011 1
11100001 00001010 0
11100000 11000001 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:
10000111 11001001 0
10100100 10000011 0
11101010 01111001 0
01100001 10000010 1
10000111 01010101 0
00101111 11100100 1
1. The parity bits for the 16 columns is: 00101111 11100100
2. The parity bits for the 5 rows is: 00010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (12,3):
01010001 00001001 1
10101001 00000010 1
10111110 00011011 0
11100101 10011000 1
10000001 01000000 1
00100010 11000000 0
For figure 3, the bit that was flipped is (6,1):
01110001 11101000 0
10101111 10110100 1
01101110 01111100 0
10110011 11101011 1
11100001 00001010 0
11100000 11000001 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: 0010111111100100
The answer was: 00010
The answer was: 1
The answer was: 12,3
The answer was: Yes