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 100011001 11100000
01101001 10100011
00111011 10101000
10110101 00011111
01011101 11001011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01000100 00010010 000101111 11000101 1
10101001 10011001 0
11010111 01011101 1
01011110 11010000 0
00001011 11000011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01001000 10000000 011011000 00110110 0
01111100 00011010 0
11100101 10001100 0
00010000 10010010 0
00011000 10110010 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:
00011001 11100000 0
01101001 10100011 0
00111011 10101000 0
10110101 00011111 0
01011101 11001011 0
10100011 00111111 0
1. The parity bits for the 16 columns is: 10100011 00111111
2. The parity bits for the 5 rows is: 00000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (1,5):
01000100 00010010 0
00101111 11000101 1
10101001 10011001 0
11010111 01011101 1
01011110 11010000 0
00001011 11000011 0
For figure 3, the bit that was flipped is (7,0):
01001000 10000000 0
11011000 00110110 0
01111100 00011010 0
11100101 10001100 0
00010000 10010010 0
00011000 10110010 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: 1010001100111111
The answer was: 00000
The answer was: 0
The answer was: 1,5
The answer was: Yes