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 111111100 00111100
01100010 00011011
10100101 11101101
01101111 01011110
10011000 10001000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110000 11110111 100110010 11001111 0
00011110 00010010 0
01001101 10011101 1
01100000 01011100 0
11100001 11101011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000101 01011010 001010010 00000100 0
01010100 00111001 1
01011110 00101001 0
10100000 01100001 1
00111101 00101111 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:
11111100 00111100 0
01100010 00011011 1
10100101 11101101 0
01101111 01011110 1
10011000 10001000 1
11001100 00011100 1
1. The parity bits for the 16 columns is: 11001100 00011100
2. The parity bits for the 5 rows is: 01011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (3,1):
11110000 11110111 1
00110010 11001111 0
00011110 00010010 0
01001101 10011101 1
01100000 01011100 0
11100001 11101011 0
For figure 3, the bit that was flipped is (1,0):
10000101 01011010 0
01010010 00000100 0
01010100 00111001 1
01011110 00101001 0
10100000 01100001 1
00111101 00101111 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: 1100110000011100
The answer was: 01011
The answer was: 1
The answer was: 3,1
The answer was: Yes