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 101000100 11100000
00110000 01101001
00110110 00101100
11110101 01110001
01010001 11111000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11001001 00000010 101111000 01101110 1
11100010 01000110 1
01010001 11000100 0
00111100 11101011 0
00111110 00010101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00110000 00011011 011001101 11000010 0
11000011 11001000 1
01010101 10101010 0
00100101 11110100 0
01001110 11001111 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:
01000100 11100000 1
00110000 01101001 0
00110110 00101100 1
11110101 01110001 0
01010001 11111000 0
11100110 00101100 0
1. The parity bits for the 16 columns is: 11100110 00101100
2. The parity bits for the 5 rows is: 10100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,5):
11001001 00000010 1
01111000 01101110 1
11100010 01000110 1
01010001 11000100 0
00111100 11101011 0
00111110 00010101 1
For figure 3, the bit that was flipped is (8,5):
00110000 00011011 0
11001101 11000010 0
11000011 11001000 1
01010101 10101010 0
00100101 11110100 0
01001110 11001111 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: 1110011000101100
The answer was: 10100
The answer was: 0
The answer was: 11,5
The answer was: Yes