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 111011101 00111000
10011100 10001110
11011111 11100001
00010110 01101110
01000101 11101000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10111001 00101000 101100001 00111100 1
10010001 11000010 1
10110011 00111010 1
00100001 10110100 0
11011011 01111000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110000 10000111 010110100 01110001 0
00100110 00110001 0
00111101 00000000 1
11100100 01010111 1
00111011 10011000 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:
11011101 00111000 1
10011100 10001110 0
11011111 11100001 1
00010110 01101110 0
01000101 11101000 1
11001101 11010001 1
1. The parity bits for the 16 columns is: 11001101 11010001
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 (10,2):
10111001 00101000 1
01100001 00111100 1
10010001 11000010 1
10110011 00111010 1
00100001 10110100 0
11011011 01111000 0
For figure 3, the bit that was flipped is (12,0):
01110000 10000111 0
10110100 01110001 0
00100110 00110001 0
00111101 00000000 1
11100100 01010111 1
00111011 10011000 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: 1100110111010001
The answer was: 10101
The answer was: 1
The answer was: 10,2
The answer was: Yes