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 110011110 10110000
00100010 11110111
00000001 11000000
01001011 11111100
00001001 11101010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10110001 10011010 011101100 00011100 0
01011000 11001111 1
11101001 10011110 0
01100111 00100110 0
00001011 11110001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100011 10101100 010111001 10011110 1
10111111 00010001 1
11100100 00100101 1
10001001 01010101 1
10001000 01010011 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:
10011110 10110000 0
00100010 11110111 1
00000001 11000000 1
01001011 11111100 0
00001001 11101010 1
11111111 10010001 1
1. The parity bits for the 16 columns is: 11111111 10010001
2. The parity bits for the 5 rows is: 01101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,5):
10110001 10011010 0
11101100 00011100 0
01011000 11001111 1
11101001 10011110 0
01100111 00100110 0
00001011 11110001 1
For figure 3, the bit that was flipped is (1,1):
10100011 10101100 0
10111001 10011110 1
10111111 00010001 1
11100100 00100101 1
10001001 01010101 1
10001000 01010011 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: 1111111110010001
The answer was: 01101
The answer was: 1
The answer was: 0,5
The answer was: Yes