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 101110100 00010011
11011010 10011011
10101101 10111111
11101101 10001100
11111001 00101111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001101 01001101 110010010 01000001 1
10111101 01011000 1
11101111 11101010 0
00010110 10010110 1
10011011 00101010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10110000 11100001 101111110 11101000 0
00100000 10110100 1
10111010 11000010 0
11111000 01111001 0
10101100 10000110 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:
01110100 00010011 1
11011010 10011011 0
10101101 10111111 0
11101101 10001100 1
11111001 00101111 1
00010111 10010100 1
1. The parity bits for the 16 columns is: 00010111 10010100
2. The parity bits for the 5 rows is: 10011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (14,0):
01001101 01001101 1
10010010 01000001 1
10111101 01011000 1
11101111 11101010 0
00010110 10010110 1
10011011 00101010 0
For figure 3, the bit that was flipped is (8,5):
10110000 11100001 1
01111110 11101000 0
00100000 10110100 1
10111010 11000010 0
11111000 01111001 0
10101100 10000110 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: 0001011110010100
The answer was: 10011
The answer was: 1
The answer was: 14,0
The answer was: Yes