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 101010100 10111101
00011100 10001100
01011011 01001110
01010000 11010000
11011100 10000001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11000001 10111101 010100010 01111011 1
01111111 00000001 0
00001001 01100110 0
01101010 10011110 1
01111111 00101111 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11001110 11011100 001011100 11111100 0
11110010 01001011 1
11100111 01100001 1
10011001 00100000 0
10011110 00101010 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:
01010100 10111101 1
00011100 10001100 0
01011011 01001110 1
01010000 11010000 1
11011100 10000001 1
10011111 00101110 0
1. The parity bits for the 16 columns is: 10011111 00101110
2. The parity bits for the 5 rows is: 10111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,0):
11000001 10111101 0
10100010 01111011 1
01111111 00000001 0
00001001 01100110 0
01101010 10011110 1
01111111 00101111 0
For figure 3, the bit that was flipped is (0,4):
11001110 11011100 0
01011100 11111100 0
11110010 01001011 1
11100111 01100001 1
10011001 00100000 0
10011110 00101010 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: 1001111100101110
The answer was: 10111
The answer was: 0
The answer was: 11,0
The answer was: Yes