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 111001011 10110101
01011111 10011011
10010011 01100100
01000010 00110001
01111010 00111110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00110001 10101001 110010010 10100011 0
00101100 10100011 1
00100111 00100010 0
10111000 10110100 0
00010000 10111111 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000100 01100000 111111011 01001001 0
00101000 01100101 1
10101000 01001111 0
10010010 10010000 1
00101101 10011011 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:
11001011 10110101 0
01011111 10011011 1
10010011 01100100 1
01000010 00110001 1
01111010 00111110 0
00111111 01000101 1
1. The parity bits for the 16 columns is: 00111111 01000101
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (8,1):
00110001 10101001 1
10010010 10100011 0
00101100 10100011 1
00100111 00100010 0
10111000 10110100 0
00010000 10111111 0
For figure 3, the bit that was flipped is (12,2):
11000100 01100000 1
11111011 01001001 0
00101000 01100101 1
10101000 01001111 0
10010010 10010000 1
00101101 10011011 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: 0011111101000101
The answer was: 01110
The answer was: 1
The answer was: 8,1
The answer was: Yes