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 110101101 00010100
11111101 11100100
00101101 10001010
11100111 10100100
00000001 01010010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01111010 00110111 001000001 11000110 0
00100101 10101000 0
10010011 11000010 1
11001001 01101100 0
01000100 11110101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01010001 11101010 000001101 11101110 1
11011110 01111010 0
01110000 11010001 1
01000101 01111000 1
10111111 11010111 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:
10101101 00010100 1
11111101 11100100 1
00101101 10001010 1
11100111 10100100 1
00000001 01010010 0
10011011 10001100 0
1. The parity bits for the 16 columns is: 10011011 10001100
2. The parity bits for the 5 rows is: 11110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,5):
01111010 00110111 0
01000001 11000110 0
00100101 10101000 0
10010011 11000010 1
11001001 01101100 0
01000100 11110101 1
For figure 3, the bit that was flipped is (4,2):
01010001 11101010 0
00001101 11101110 1
11011110 01111010 0
01110000 11010001 1
01000101 01111000 1
10111111 11010111 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: 1001101110001100
The answer was: 11110
The answer was: 0
The answer was: 14,5
The answer was: Yes