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 101111010 01100011
11100000 10000100
11011100 01000111
10111000 11101110
01100101 11010111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111110 01111110 101010110 00000001 1
11110010 10101011 0
10010110 00010111 0
00100100 00010000 1
11101010 11010011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00001011 01111001 101000001 01000101 1
01000001 01011101 1
00100001 11001110 1
00011001 11111011 0
00110011 10010100 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:
01111010 01100011 1
11100000 10000100 1
11011100 01000111 1
10111000 11101110 0
01100101 11010111 0
10011011 10011001 1
1. The parity bits for the 16 columns is: 10011011 10011001
2. The parity bits for the 5 rows is: 11100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (6,5):
11111110 01111110 1
01010110 00000001 1
11110010 10101011 0
10010110 00010111 0
00100100 00010000 1
11101010 11010011 1
For figure 3, the bits that were flipped are (8,5) and (9,0):
00001011 01111001 1
01000001 01000101 1
01000001 01011101 1
00100001 11001110 1
00011001 11111011 0
00110011 10010100 0
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 1001101110011001
The answer was: 11100
The answer was: 1
The answer was: 6,5
The answer was: No