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 100010000 00110111
10101000 00000111
11100011 10110100
00101111 10001111
11001010 11110100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001011 00111011 110111101 01100100 1
01110111 11011111 0
11101100 01010101 1
01011000 11100011 0
00110101 00110100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100001 01100011 100010100 00001100 0
01010000 10000001 0
11100100 00101100 0
11011001 11001011 0
11011010 00001001 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:
00010000 00110111 0
10101000 00000111 0
11100011 10110100 1
00101111 10001111 0
11001010 11110100 1
10111110 11111111 0
1. The parity bits for the 16 columns is: 10111110 11111111
2. The parity bits for the 5 rows is: 00101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,2):
01001011 00111011 1
10111101 01100100 1
01110111 11011111 0
11101100 01010101 1
01011000 11100011 0
00110101 00110100 1
For figure 3, the bits that were flipped are (6,5) and (16,3):
10100001 01100011 1
00010100 00001100 0
01010000 10000001 0
11100100 00101100 0
11011001 11001011 0
11011010 00001001 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: 1011111011111111
The answer was: 00101
The answer was: 0
The answer was: 14,2
The answer was: No