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 111010111 10100111
10111000 11100100
11001001 10110011
10010111 01111110
00110000 10000110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01111100 11010010 100101011 00110101 0
10010001 01000011 0
01100100 10010111 0
10001100 10101010 0
00101110 10001001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00010010 00010000 110101110 00000010 0
01101001 00111001 1
10000011 11100011 0
00101010 00101111 0
01111101 11100111 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:
11010111 10100111 1
10111000 11100100 0
11001001 10110011 1
10010111 01111110 1
00110000 10000110 1
00000001 00001000 0
1. The parity bits for the 16 columns is: 00000001 00001000
2. The parity bits for the 5 rows is: 10111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,4):
01111100 11010010 1
00101011 00110101 0
10010001 01000011 0
01100100 10010111 0
10001100 10101010 0
00101110 10001001 1
For figure 3, the bit that was flipped is (7,2):
00010010 00010000 1
10101110 00000010 0
01101001 00111001 1
10000011 11100011 0
00101010 00101111 0
01111101 11100111 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0000000100001000
The answer was: 10111
The answer was: 0
The answer was: 11,4
The answer was: Yes