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 100111101 11001111
00101001 01111000
00010110 11111000
00000001 00001100
01000001 01001101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11100000 01100101 100001001 01001100 1
11110000 01110110 1
00011011 00110101 0
00011010 11001110 0
00011000 10100000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00111010 11010010 000111000 00010000 0
00010001 11101010 1
00101110 01000101 1
11010011 00010010 0
11101110 01111110 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:
00111101 11001111 1
00101001 01111000 1
00010110 11111000 0
00000001 00001100 1
01000001 01001101 0
01000010 00001110 1
1. The parity bits for the 16 columns is: 01000010 00001110
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,5):
11100000 01100101 1
00001001 01001100 1
11110000 01110110 1
00011011 00110101 0
00011010 11001110 0
00011000 10100000 1
For figure 3, the bit that was flipped is (15,4):
00111010 11010010 0
00111000 00010000 0
00010001 11101010 1
00101110 01000101 1
11010011 00010010 0
11101110 01111110 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: 0100001000001110
The answer was: 11010
The answer was: 1
The answer was: 13,5
The answer was: Yes