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 101011011 00100011
00110001 00011000
11000111 00101000
00001111 11100110
11111011 00111011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00000011 11100110 000110000 01000011 1
01110101 00101001 0
01010010 10101110 0
11010110 01100111 0
11010010 01000101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10011010 11110100 000101010 01110001 1
01001000 10010011 0
11010110 10100100 0
10100010 01010100 0
10101100 11100110 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:
01011011 00100011 0
00110001 00011000 1
11000111 00101000 1
00001111 11100110 1
11111011 00111011 0
01011001 11001110 1
1. The parity bits for the 16 columns is: 01011001 11001110
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 (3,0):
00000011 11100110 0
00110000 01000011 1
01110101 00101001 0
01010010 10101110 0
11010110 01100111 0
11010010 01000101 1
For figure 3, the bit that was flipped is (2,0):
10011010 11110100 0
00101010 01110001 1
01001000 10010011 0
11010110 10100100 0
10100010 01010100 0
10101100 11100110 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: 0101100111001110
The answer was: 01110
The answer was: 1
The answer was: 3,0
The answer was: Yes