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 100010010 10010001
10111100 11100110
01011100 01000011
00110001 11101111
00100101 11110011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10100011 01010111 001001001 10101101 0
01011110 10110000 0
10011011 01000001 1
10000100 10000110 1
00101011 10001101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11111110 10001100 000101010 10011000 0
10100010 00000101 1
00011001 11001100 1
11010111 00001111 0
10101000 11010010 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:
00010010 10010001 1
10111100 11100110 0
01011100 01000011 1
00110001 11101111 0
00100101 11110011 1
11100110 00101000 1
1. The parity bits for the 16 columns is: 11100110 00101000
2. The parity bits for the 5 rows is: 10101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,0):
10100011 01010111 0
01001001 10101101 0
01011110 10110000 0
10011011 01000001 1
10000100 10000110 1
00101011 10001101 0
For figure 3, the bit that was flipped is (3,5):
11111110 10001100 0
00101010 10011000 0
10100010 00000101 1
00011001 11001100 1
11010111 00001111 0
10101000 11010010 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: 1110011000101000
The answer was: 10101
The answer was: 1
The answer was: 0,0
The answer was: Yes