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 100000110 00010101
01000011 11000000
01100010 11111001
11000010 10110000
11100111 11110100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10100000 10011010 011111111 11000011 0
10111110 11011110 0
11100100 10000101 1
00101100 01001111 0
00100001 01001101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01101111 11000010 110001100 01010111 0
11100111 00101101 0
10010001 11000111 0
01011001 00100011 1
11001100 11011100 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:
00000110 00010101 1
01000011 11000000 1
01100010 11111001 1
11000010 10110000 0
11100111 11110100 1
00000010 01101000 0
1. The parity bits for the 16 columns is: 00000010 01101000
2. The parity bits for the 5 rows is: 11101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (4,5):
10100000 10011010 0
11111111 11000011 0
10111110 11011110 0
11100100 10000101 1
00101100 01001111 0
00100001 01001101 1
For figure 3, the bit that was flipped is (8,5):
01101111 11000010 1
10001100 01010111 0
11100111 00101101 0
10010001 11000111 0
01011001 00100011 1
11001100 11011100 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: 0000001001101000
The answer was: 11101
The answer was: 0
The answer was: 4,5
The answer was: Yes