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 111011011 10011101
01100111 01101110
00111101 10010011
01010011 01010101
11001001 11011001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011111 00111010 010011110 00000011 1
10110000 01011011 1
01010110 00011000 0
00000100 01010111 0
11000011 00101101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00000001 01111000 110000011 11100110 0
11011100 01001101 1
11100000 00110011 0
01100101 11000001 1
11011011 00100001 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:
11011011 10011101 1
01100111 01101110 0
00111101 10010011 1
01010011 01010101 0
11001001 11011001 1
00011011 11101100 1
1. The parity bits for the 16 columns is: 00011011 11101100
2. The parity bits for the 5 rows is: 10101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (2,2):
10011111 00111010 0
10011110 00000011 1
10110000 01011011 1
01010110 00011000 0
00000100 01010111 0
11000011 00101101 0
For figure 3, the bit that was flipped is (16,3):
00000001 01111000 1
10000011 11100110 0
11011100 01001101 1
11100000 00110011 0
01100101 11000001 1
11011011 00100001 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: 0001101111101100
The answer was: 10101
The answer was: 1
The answer was: 2,2
The answer was: Yes