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 101100001 11001011
11011111 11001100
01010000 01100010
11111001 01100101
01101001 01010000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11000001 00000010 111101010 11111100 1
01101101 00110011 1
11100010 10010010 1
00010111 11010011 1
10110010 10001100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01001010 01110101 001010111 01110010 0
01001010 01100000 1
10111000 00011011 0
00100100 10011101 1
11001011 01100001 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:
01100001 11001011 0
11011111 11001100 1
01010000 01100010 1
11111001 01100101 0
01101001 01010000 0
01111110 01010000 0
1. The parity bits for the 16 columns is: 01111110 01010000
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 (7,0):
11000001 00000010 1
11101010 11111100 1
01101101 00110011 1
11100010 10010010 1
00010111 11010011 1
10110010 10001100 1
For figure 3, the bit that was flipped is (8,1):
01001010 01110101 0
01010111 01110010 0
01001010 01100000 1
10111000 00011011 0
00100100 10011101 1
11001011 01100001 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: 0111111001010000
The answer was: 01100
The answer was: 0
The answer was: 7,0
The answer was: Yes