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 111001100 10010010
11001100 11001110
11100101 01101101
00110100 11010000
11010011 01001101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011011 01011010 110010111 11100010 1
11001111 11101110 0
11110110 10011110 1
11101010 00111111 0
11011011 11110111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011001 01010110 101111000 01000100 0
00011001 01010001 1
10000000 10110010 1
11101000 11101001 1
00010000 00011001 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:
11001100 10010010 1
11001100 11001110 1
11100101 01101101 0
00110100 11010000 0
11010011 01001101 1
00000010 10101100 1
1. The parity bits for the 16 columns is: 00000010 10101100
2. The parity bits for the 5 rows is: 11001
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (5,4):
10011011 01011010 1
10010111 11100010 1
11001111 11101110 0
11110110 10011110 1
11101010 00111111 0
11011011 11110111 1
For figure 3, the bit that was flipped is (15,2):
00011001 01010110 1
01111000 01000100 0
00011001 01010001 1
10000000 10110010 1
11101000 11101001 1
00010000 00011001 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: 0000001010101100
The answer was: 11001
The answer was: 1
The answer was: 5,4
The answer was: Yes