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 111101111 10110111
01010010 00011101
01000111 10000101
11100100 01000001
00001001 11100101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01000100 01011010 000000000 10100011 0
11111101 01010101 1
11000001 01101110 0
00110111 00110100 0
01001101 11110110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11001011 10100101 011101001 01100101 1
11001000 01100110 1
01011000 10101011 0
10001100 11010111 1
00011110 01011010 1
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:
11101111 10110111 1
01010010 00011101 1
01000111 10000101 1
11100100 01000001 0
00001001 11100101 1
00010111 10001011 0
1. The parity bits for the 16 columns is: 00010111 10001011
2. The parity bits for the 5 rows is: 11101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (6,5):
01000100 01011010 0
00000000 10100011 0
11111101 01010101 1
11000001 01101110 0
00110111 00110100 0
01001101 11110110 1
For figure 3, the bits that were flipped are (8,5) and (2,0):
11001011 10100101 0
11101001 01100101 1
11001000 01100110 1
01011000 10101011 0
10001100 11010111 1
00011110 01011010 1
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: 0001011110001011
The answer was: 11101
The answer was: 0
The answer was: 6,5
The answer was: No