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 111010101 11011010
01110010 01011001
00011011 11001011
10011001 01101100
11010011 10101111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001001 11001111 100000000 11110101 0
11000011 00011001 1
10000000 11010110 0
11101000 01101110 0
11100010 10011011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10110000 10110111 000101111 10110010 1
11000101 01010111 1
01000000 00111001 1
01100010 11010111 1
01011000 10111100 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:
11010101 11011010 0
01110010 01011001 0
00011011 11001011 1
10011001 01101100 0
11010011 10101111 1
11110110 10001011 0
1. The parity bits for the 16 columns is: 11110110 10001011
2. The parity bits for the 5 rows is: 00101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,4):
01001001 11001111 1
00000000 11110101 0
11000011 00011001 1
10000000 11010110 0
11101000 01101110 0
11100010 10011011 1
For figure 3, the bit that was flipped is (2,0):
10110000 10110111 0
00101111 10110010 1
11000101 01010111 1
01000000 00111001 1
01100010 11010111 1
01011000 10111100 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: 1111011010001011
The answer was: 00101
The answer was: 0
The answer was: 16,4
The answer was: Yes