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 111001100 11010000
11000101 01000101
01111001 10000101
10001110 00011001
10001110 00011011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011011 11110001 000000110 00110000 1
00010000 11100000 0
10001110 00100011 1
11001110 01001011 1
11001101 01001011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000010 11001011 100110111 01001100 0
01000100 00011011 0
00010100 01100111 1
10010100 11010000 1
10110001 00111011 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:
11001100 11010000 1
11000101 01000101 1
01111001 10000101 0
10001110 00011001 1
10001110 00011011 0
01110000 00010010 1
1. The parity bits for the 16 columns is: 01110000 00010010
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (14,1):
10011011 11110001 0
00000110 00110000 1
00010000 11100000 0
10001110 00100011 1
11001110 01001011 1
11001101 01001011 1
For figure 3, the bit that was flipped is (11,4):
01000010 11001011 1
00110111 01001100 0
01000100 00011011 0
00010100 01100111 1
10010100 11010000 1
10110001 00111011 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: 0111000000010010
The answer was: 11010
The answer was: 1
The answer was: 14,1
The answer was: Yes