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 111110110 00101111
11000110 10110111
00010100 00011101
01010100 01111001
01110111 00110111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11001110 10010101 001011011 11111100 1
11001111 10010111 1
00100011 10001000 1
11010001 11000110 0
10101000 10110100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00100011 10001001 110110001 01000000 1
11111110 10001110 1
11101110 01101110 1
11001100 11110100 1
01001110 11011111 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:
11110110 00101111 1
11000110 10110111 0
00010100 00011101 0
01010100 01111001 0
01110111 00110111 1
00000111 11001011 0
1. The parity bits for the 16 columns is: 00000111 11001011
2. The parity bits for the 5 rows is: 10001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (13,0):
11001110 10010101 0
01011011 11111100 1
11001111 10010111 1
00100011 10001000 1
11010001 11000110 0
10101000 10110100 1
For figure 3, the bit that was flipped is (14,0):
00100011 10001001 1
10110001 01000000 1
11111110 10001110 1
11101110 01101110 1
11001100 11110100 1
01001110 11011111 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: 0000011111001011
The answer was: 10001
The answer was: 0
The answer was: 13,0
The answer was: Yes