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 101000011 00111000
11000110 00000000
11001001 11000011
01100101 00011001
10111000 10001000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00110001 10001001 001111100 00111111 0
11000101 00010101 1
01010100 01010000 1
10110010 11001100 0
01101110 00111011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100011 11010010 110100000 00100010 0
11111111 01111000 0
00000011 01111111 1
10101000 11100000 0
01011111 00010111 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:
01000011 00111000 0
11000110 00000000 0
11001001 11000011 0
01100101 00011001 1
10111000 10001000 0
10010001 01101010 1
1. The parity bits for the 16 columns is: 10010001 01101010
2. The parity bits for the 5 rows is: 00010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,1):
00110001 10001001 0
01111100 00111111 0
11000101 00010101 1
01010100 01010000 1
10110010 11001100 0
01101110 00111011 0
For figure 3, the bit that was flipped is (4,0):
10100011 11010010 1
10100000 00100010 0
11111111 01111000 0
00000011 01111111 1
10101000 11100000 0
01011111 00010111 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: 1001000101101010
The answer was: 00010
The answer was: 1
The answer was: 13,1
The answer was: Yes