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 110011010 11101010
10000100 00010111
01011010 00100000
00100000 11000010
00001001 01010011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111111 00001010 100000110 00110110 0
10001010 10101010 1
00111000 01011010 1
01010110 01101001 0
00011101 10110101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10010101 01110100 011000110 00111001 0
01101100 10100111 1
00110010 01100111 1
10100000 10000101 1
10101001 00001000 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:
10011010 11101010 1
10000100 00010111 0
01011010 00100000 1
00100000 11000010 0
00001001 01010011 0
01101101 01001100 0
1. The parity bits for the 16 columns is: 01101101 01001100
2. The parity bits for the 5 rows is: 10100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,0):
11111111 00001010 1
00000110 00110110 0
10001010 10101010 1
00111000 01011010 1
01010110 01101001 0
00011101 10110101 1
For figure 3, the bit that was flipped is (5,3):
10010101 01110100 0
11000110 00111001 0
01101100 10100111 1
00110010 01100111 1
10100000 10000101 1
10101001 00001000 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: 0110110101001100
The answer was: 10100
The answer was: 0
The answer was: 11,0
The answer was: Yes