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 100101001 00101010
10000001 01000100
01100111 00100101
10110010 10001101
10011100 10011100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10110101 11101101 100110101 00100100 0
11100110 01000010 0
11010010 10010001 1
00101000 00111011 1
10011000 00100001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000100 11000010 000001101 10011111 0
11011010 01011000 0
10010101 01110100 0
01101101 01001011 0
11101011 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:
00101001 00101010 0
10000001 01000100 0
01100111 00100101 0
10110010 10001101 0
10011100 10011100 0
11100001 01011010 0
1. The parity bits for the 16 columns is: 11100001 01011010
2. The parity bits for the 5 rows is: 00000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (5,2):
10110101 11101101 1
00110101 00100100 0
11100110 01000010 0
11010010 10010001 1
00101000 00111011 1
10011000 00100001 1
For figure 3, the bits that were flipped are (10,1) and (9,4):
11000100 11000010 0
00001101 10011111 0
11011010 01011000 0
10010101 01110100 0
01101101 01001011 0
11101011 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: 1110000101011010
The answer was: 00000
The answer was: 0
The answer was: 5,2
The answer was: No