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 100000100 10101110
01100111 10111000
01110011 01010011
01000000 01011001
10001110 10000111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11101001 10010011 100110100 10001100 1
00011101 00101010 1
11011110 11000011 0
11111010 11010101 1
11100100 00100001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01010111 10100110 100101100 00100111 0
11100110 00101100 0
10101000 11111101 0
10111100 10101100 1
00001000 11111100 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:
00000100 10101110 0
01100111 10111000 1
01110011 01010011 1
01000000 01011001 1
10001110 10000111 0
11011110 10011011 1
1. The parity bits for the 16 columns is: 11011110 10011011
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (14,1):
11101001 10010011 1
00110100 10001100 1
00011101 00101010 1
11011110 11000011 0
11111010 11010101 1
11100100 00100001 0
For figure 3, the bits that were flipped are (7,5) and (0,1):
01010111 10100110 1
00101100 00100111 0
11100110 00101100 0
10101000 11111101 0
10111100 10101100 1
00001000 11111100 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: 1101111010011011
The answer was: 01110
The answer was: 1
The answer was: 14,1
The answer was: No