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 100110010 11111000
10001101 01100000
11101000 11010101
00111000 00111110
00001010 10101111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110110 00000000 011000110 01100000 0
11011100 10011010 1
00001010 00111111 1
11101111 01101101 0
00101001 10101000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00111010 11011100 011100101 00100011 0
11001101 10011010 1
10000111 11011010 1
00011100 10101001 1
10001101 00010110 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:
00110010 11111000 0
10001101 01100000 0
11101000 11010101 1
00111000 00111110 0
00001010 10101111 0
01100101 11011100 1
1. The parity bits for the 16 columns is: 01100101 11011100
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 (2,3):
11110110 00000000 0
11000110 01100000 0
11011100 10011010 1
00001010 00111111 1
11101111 01101101 0
00101001 10101000 0
For figure 3, the bit that was flipped is (5,0):
00111010 11011100 0
11100101 00100011 0
11001101 10011010 1
10000111 11011010 1
00011100 10101001 1
10001101 00010110 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: 0110010111011100
The answer was: 00100
The answer was: 1
The answer was: 2,3
The answer was: Yes