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 111011100 00101101
00110110 10110101
10100010 11010010
10101111 00010111
10011111 11001001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10101101 11011100 001111001 10111100 0
11001100 10100101 0
00000101 00011111 0
00011000 11111000 1
10000101 00100010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10001011 10000011 110010101 10100111 1
11001111 10110011 1
10001000 00100000 1
01110111 11000110 0
00101110 01110101 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:
11011100 00101101 1
00110110 10110101 1
10100010 11010010 1
10101111 00010111 0
10011111 11001001 0
01111000 10010100 1
1. The parity bits for the 16 columns is: 01111000 10010100
2. The parity bits for the 5 rows is: 11100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,3):
10101101 11011100 0
01111001 10111100 0
11001100 10100101 0
00000101 00011111 0
00011000 11111000 1
10000101 00100010 1
For figure 3, the bit that was flipped is (13,5):
10001011 10000011 1
10010101 10100111 1
11001111 10110011 1
10001000 00100000 1
01110111 11000110 0
00101110 01110101 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: 0111100010010100
The answer was: 11100
The answer was: 1
The answer was: 0,3
The answer was: Yes