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 00110000
10110100 01011100
00001101 00100001
10011011 01011101
01010011 01111000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11010100 11011010 111010001 10001000 1
11110101 10010100 1
10111101 10010000 0
01111001 00010001 1
00010100 01000111 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101100 01100101 101111101 01110000 1
00110001 11000001 0
01011001 00011111 1
10110111 11010011 0
01001110 00011010 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:
01100011 00110000 0
10110100 01011100 0
00001101 00100001 1
10011011 01011101 0
01010011 01111000 0
00010010 01101000 1
1. The parity bits for the 16 columns is: 00010010 01101000
2. The parity bits for the 5 rows is: 00100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (2,1):
11010100 11011010 1
11010001 10001000 1
11110101 10010100 1
10111101 10010000 0
01111001 00010001 1
00010100 01000111 0
For figure 3, the bit that was flipped is (14,4):
11101100 01100101 1
01111101 01110000 1
00110001 11000001 0
01011001 00011111 1
10110111 11010011 0
01001110 00011010 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: 0001001001101000
The answer was: 00100
The answer was: 1
The answer was: 2,1
The answer was: Yes