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 110010000 11001011
11110111 01011000
11010011 10110000
00010000 11001101
00110011 01111001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010111 00001000 011100101 11011001 0
11101010 00111110 0
01110011 01101010 1
10010001 10011000 1
01110010 00011101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01011100 10011001 001101100 11010001 0
10000001 00000011 0
01001101 10111000 0
11000010 00001100 0
00111110 11011111 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:
10010000 11001011 1
11110111 01011000 0
11010011 10110000 0
00010000 11001101 0
00110011 01111001 1
10010111 10010111 0
1. The parity bits for the 16 columns is: 10010111 10010111
2. The parity bits for the 5 rows is: 10001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (4,4):
10010111 00001000 0
11100101 11011001 0
11101010 00111110 0
01110011 01101010 1
10010001 10011000 1
01110010 00011101 0
For figure 3, the bit that was flipped is (10,4):
01011100 10011001 0
01101100 11010001 0
10000001 00000011 0
01001101 10111000 0
11000010 00001100 0
00111110 11011111 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: 1001011110010111
The answer was: 10001
The answer was: 0
The answer was: 4,4
The answer was: Yes