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 100010011 00101110
10010111 00111011
00001111 01001110
10101110 00001010
00111000 11101101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10000100 00010011 000101001 00111000 0
10001011 11011001 1
11001011 11010010 1
11111110 10010000 1
00010010 10110000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00000110 00000110 011010101 00110100 0
00111010 11000010 1
10111101 11010111 1
01011010 01000100 1
01001100 01100011 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:
00010011 00101110 1
10010111 00111011 0
00001111 01001110 0
10101110 00001010 1
00111000 11101101 1
00011101 10111100 1
1. The parity bits for the 16 columns is: 00011101 10111100
2. The parity bits for the 5 rows is: 10011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (7,0):
10000100 00010011 0
00101001 00111000 0
10001011 11011001 1
11001011 11010010 1
11111110 10010000 1
00010010 10110000 1
For figure 3, the bits that were flipped are (1,4) and (6,3):
00000110 00000110 0
11010101 00110100 0
00111010 11000010 1
10111101 11010111 1
01011010 01000100 1
01001100 01100011 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: 0001110110111100
The answer was: 10011
The answer was: 1
The answer was: 7,0
The answer was: No