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 100111101 11000110
11101100 11001000
00000011 11011011
01000111 11011011
10110110 00011110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111001 11111111 001001100 00111011 0
10010101 10011011 1
00101010 10000101 0
10011011 00111011 1
10010001 11100011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011100 01011111 011100000 01000110 0
10110100 01100001 1
11001001 11011000 0
01010001 01001100 0
11010000 11111100 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:
00111101 11000110 1
11101100 11001000 0
00000011 11011011 0
01000111 11011011 0
10110110 00011110 1
00100011 00010000 0
1. The parity bits for the 16 columns is: 00100011 00010000
2. The parity bits for the 5 rows is: 10001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,4):
11111001 11111111 0
01001100 00111011 0
10010101 10011011 1
00101010 10000101 0
10011011 00111011 1
10010001 11100011 0
For figure 3, the bit that was flipped is (11,0):
00011100 01011111 0
11100000 01000110 0
10110100 01100001 1
11001001 11011000 0
01010001 01001100 0
11010000 11111100 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0010001100010000
The answer was: 10001
The answer was: 0
The answer was: 14,4
The answer was: Yes