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 101000101 00100000
10011101 10010000
00111001 10001010
11101001 01000000
01100010 11111011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10101111 10100111 110111011 01100010 0
01101000 11010101 0
00000101 00111101 1
01110111 10100111 1
00001110 10001010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110101 10101001 111001111 01111010 0
11100010 11101101 0
00000101 00000000 0
01011110 11111001 1
00000011 11000011 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:
01000101 00100000 0
10011101 10010000 1
00111001 10001010 1
11101001 01000000 0
01100010 11111011 0
01101010 10000001 0
1. The parity bits for the 16 columns is: 01101010 10000001
2. The parity bits for the 5 rows is: 01100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,1):
10101111 10100111 1
10111011 01100010 0
01101000 11010101 0
00000101 00111101 1
01110111 10100111 1
00001110 10001010 0
For figure 3, the bit that was flipped is (13,1):
01110101 10101001 1
11001111 01111010 0
11100010 11101101 0
00000101 00000000 0
01011110 11111001 1
00000011 11000011 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: 0110101010000001
The answer was: 01100
The answer was: 0
The answer was: 16,1
The answer was: Yes