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 110011101 01000101
01000100 11100010
00010010 01111101
00100010 01111110
10110100 01011000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01111010 11010011 001000011 00100010 1
10010101 11010001 1
00100110 10010111 0
00011111 01001010 0
10010101 01111101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01101111 01111000 101100111 11001100 1
10011010 01001010 1
11000011 11000101 1
10011001 11110010 1
11001010 11001000 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:
10011101 01000101 0
01000100 11100010 0
00010010 01111101 0
00100010 01111110 0
10110100 01011000 1
01011101 11111100 1
1. The parity bits for the 16 columns is: 01011101 11111100
2. The parity bits for the 5 rows is: 00001
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (8,2):
01111010 11010011 0
01000011 00100010 1
10010101 11010001 1
00100110 10010111 0
00011111 01001010 0
10010101 01111101 0
For figure 3, the bits that were flipped are (6,0) and (15,3):
01101111 01111000 1
01100111 11001100 1
10011010 01001010 1
11000011 11000101 1
10011001 11110010 1
11001010 11001000 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: 0101110111111100
The answer was: 00001
The answer was: 1
The answer was: 8,2
The answer was: No