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 101010101 11000011
11110101 00100101
01011011 00010010
00111010 00111101
01000011 00000100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01010110 01000101 110100101 00011000 0
00100100 00001100 0
11010100 00010011 0
00101000 10110011 1
00101011 01110001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11110000 11010110 000001111 01111001 1
01000000 10111011 1
11110010 10011001 1
00111000 00101111 0
01110100 10100010 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:
01010101 11000011 0
11110101 00100101 1
01011011 00010010 1
00111010 00111101 1
01000011 00000100 0
10000010 11001101 1
1. The parity bits for the 16 columns is: 10000010 11001101
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (8,3):
01010110 01000101 1
10100101 00011000 0
00100100 00001100 0
11010100 00010011 0
00101000 10110011 1
00101011 01110001 0
For figure 3, the bit that was flipped is (7,0):
11110000 11010110 0
00001111 01111001 1
01000000 10111011 1
11110010 10011001 1
00111000 00101111 0
01110100 10100010 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: 1000001011001101
The answer was: 01110
The answer was: 1
The answer was: 8,3
The answer was: Yes