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 100110011 11010011
00111110 11001001
11000101 01010111
01011110 01010101
11110100 10000100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101100 11010100 001000111 00110001 1
00000001 10001111 0
10001001 00011010 0
01000011 11101101 1
11100000 10010101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00110010 11010011 101100010 10111001 0
10101010 10100011 1
00110001 01010011 1
11000000 10101110 1
00000111 00110100 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:
00110011 11010011 1
00111110 11001001 1
11000101 01010111 1
01011110 01010101 1
11110100 10000100 1
01100010 10011100 1
1. The parity bits for the 16 columns is: 01100010 10011100
2. The parity bits for the 5 rows is: 11111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (12,5):
01101100 11010100 0
01000111 00110001 1
00000001 10001111 0
10001001 00011010 0
01000011 11101101 1
11100000 10010101 0
For figure 3, the bits that were flipped are (4,0) and (5,2):
00110010 11010011 1
01100010 10111001 0
10101010 10100011 1
00110001 01010011 1
11000000 10101110 1
00000111 00110100 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: 0110001010011100
The answer was: 11111
The answer was: 1
The answer was: 12,5
The answer was: No