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 101000001 00010001
11100011 10000101
01101001 10110011
00001100 00101000
10000011 01111111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101011 00010100 011111100 01100000 1
01110110 10001101 1
00010011 00111001 1
10000001 10111011 0
00110011 01110011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101011 11111111 010000010 01011001 0
00011011 11010101 1
00111111 10011010 0
10000011 01111011 0
11001110 11010010 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:
01000001 00010001 0
11100011 10000101 0
01101001 10110011 1
00001100 00101000 0
10000011 01111111 0
01000100 01110000 1
1. The parity bits for the 16 columns is: 01000100 01110000
2. The parity bits for the 5 rows is: 00100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (12,1):
00101011 00010100 0
11111100 01100000 1
01110110 10001101 1
00010011 00111001 1
10000001 10111011 0
00110011 01110011 1
For figure 3, the bit that was flipped is (9,4):
11101011 11111111 0
10000010 01011001 0
00011011 11010101 1
00111111 10011010 0
10000011 01111011 0
11001110 11010010 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: 0100010001110000
The answer was: 00100
The answer was: 1
The answer was: 12,1
The answer was: Yes