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 111110110 00010010
00101110 00001011
00000100 00110101
01101101 00101101
01011110 10110011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01010110 10010111 110011011 01001000 1
10111001 01011010 1
11011000 10010100 0
10010010 00100001 1
00101110 00110000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101011 00001001 001111100 01110110 0
10110100 10110111 1
01100110 11111110 1
01000001 11010011 1
00000100 01100101 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:
11110110 00010010 0
00101110 00001011 1
00000100 00110101 1
01101101 00101101 1
01011110 10110011 0
11101111 10110010 1
1. The parity bits for the 16 columns is: 11101111 10110010
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (3,3):
01010110 10010111 1
10011011 01001000 1
10111001 01011010 1
11011000 10010100 0
10010010 00100001 1
00101110 00110000 0
For figure 3, the bit that was flipped is (8,2):
11101011 00001001 0
01111100 01110110 0
10110100 10110111 1
01100110 11111110 1
01000001 11010011 1
00000100 01100101 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: 1110111110110010
The answer was: 01110
The answer was: 1
The answer was: 3,3
The answer was: Yes