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 110001101 01000000
00100001 01011001
10110110 00001101
01010000 11000111
11001010 00101011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11101111 10100001 011010110 10001100 0
00101110 00100010 0
00101101 10110001 0
10111000 01011001 1
10000110 11100111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011000 00101110 010111011 00111000 1
00011110 00111001 0
01010010 11011001 0
01100100 00010110 1
01001011 11100000 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:
10001101 01000000 1
00100001 01011001 0
10110110 00001101 0
01010000 11000111 1
11001010 00101011 0
10000000 11111000 0
1. The parity bits for the 16 columns is: 10000000 11111000
2. The parity bits for the 5 rows is: 10010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (5,4):
11101111 10100001 0
11010110 10001100 0
00101110 00100010 0
00101101 10110001 0
10111000 01011001 1
10000110 11100111 1
For figure 3, the bit that was flipped is (16,4):
11011000 00101110 0
10111011 00111000 1
00011110 00111001 0
01010010 11011001 0
01100100 00010110 1
01001011 11100000 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: 1000000011111000
The answer was: 10010
The answer was: 0
The answer was: 5,4
The answer was: Yes