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 101100011 11010000
00111011 00011110
01100010 11111101
00000100 10100011
11010100 10010001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001111 00011000 111111001 11010010 0
00101001 10011100 1
01100100 00001111 1
11010010 11110110 0
11101001 10100111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000011 10111100 100100001 01000111 0
00000101 01001110 0
01101011 11000110 1
00011001 00100011 0
10010101 01000000 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:
01100011 11010000 1
00111011 00011110 1
01100010 11111101 0
00000100 10100011 1
11010100 10010001 1
11101010 00000001 0
1. The parity bits for the 16 columns is: 11101010 00000001
2. The parity bits for the 5 rows is: 11011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (12,5):
10001111 00011000 1
11111001 11010010 0
00101001 10011100 1
01100100 00001111 1
11010010 11110110 0
11101001 10100111 1
For figure 3, the bit that was flipped is (11,5):
11000011 10111100 1
00100001 01000111 0
00000101 01001110 0
01101011 11000110 1
00011001 00100011 0
10010101 01000000 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: 1110101000000001
The answer was: 11011
The answer was: 0
The answer was: 12,5
The answer was: Yes