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 111111001 01111011
11100011 11011110
11101110 00101011
00101110 11011100
10101100 01010101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11010001 00001101 110111001 10001111 0
10000101 00000100 0
10110000 01010000 0
00000001 10100010 0
01001100 01110100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00000110 00000111 111101110 01111010 0
10010010 11100111 1
00001110 11011010 0
00010111 10000010 0
01110011 11000010 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:
11111001 01111011 0
11100011 11011110 1
11101110 00101011 0
00101110 11011100 1
10101100 01010101 0
01110110 00000111 0
1. The parity bits for the 16 columns is: 01110110 00000111
2. The parity bits for the 5 rows is: 01010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,3):
11010001 00001101 1
10111001 10001111 0
10000101 00000100 0
10110000 01010000 0
00000001 10100010 0
01001100 01110100 1
For figure 3, the bit that was flipped is (3,1):
00000110 00000111 1
11101110 01111010 0
10010010 11100111 1
00001110 11011010 0
00010111 10000010 0
01110011 11000010 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: 0111011000000111
The answer was: 01010
The answer was: 0
The answer was: 3,3
The answer was: Yes