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 110101111 10100110
10110100 01100110
11101111 01011101
11111101 10000001
10011111 11100100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001101 11001100 011001100 10010101 0
11001110 01010111 0
10101110 01101100 1
00010001 01110001 0
00110001 00010011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101011 01100000 010110000 11111001 0
01011011 11101110 1
00101111 11101010 0
00011110 11000011 1
11110011 01011010 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:
10101111 10100110 0
10110100 01100110 0
11101111 01011101 0
11111101 10000001 1
10011111 11100100 0
10010110 11111000 1
1. The parity bits for the 16 columns is: 10010110 11111000
2. The parity bits for the 5 rows is: 00010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (7,5):
10001101 11001100 0
11001100 10010101 0
11001110 01010111 0
10101110 01101100 1
00010001 01110001 0
00110001 00010011 1
For figure 3, the bits that were flipped are (13,1) and (6,4):
00101011 01100000 0
10110000 11111001 0
01011011 11101110 1
00101111 11101010 0
00011110 11000011 1
11110011 01011010 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: 1001011011111000
The answer was: 00010
The answer was: 1
The answer was: 7,5
The answer was: No