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 101101111 10100110
00100111 10011110
01101010 01001100
01111011 00101011
00001110 00011110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11001010 01101011 110101101 00111111 1
10001110 01001100 0
00100010 00011100 1
01000111 00111011 1
10001100 00111011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00010110 11110100 010101100 11000010 0
10111111 10000010 1
01001100 11101111 0
01001011 01010001 1
00000010 00001010 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:
01101111 10100110 0
00100111 10011110 1
01101010 01001100 1
01111011 00101011 0
00001110 00011110 1
01010111 01000001 1
1. The parity bits for the 16 columns is: 01010111 01000001
2. The parity bits for the 5 rows is: 01101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,2):
11001010 01101011 1
10101101 00111111 1
10001110 01001100 0
00100010 00011100 1
01000111 00111011 1
10001100 00111011 0
For figure 3, the bit that was flipped is (16,1):
00010110 11110100 0
10101100 11000010 0
10111111 10000010 1
01001100 11101111 0
01001011 01010001 1
00000010 00001010 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: 0101011101000001
The answer was: 01101
The answer was: 1
The answer was: 13,2
The answer was: Yes