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 110110000 00000100
01011001 01100100
01001100 01101111
01010000 10101001
10100010 00000011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001010 00001110 010101100 11111011 0
00110011 10100111 1
01111010 10001001 0
11111101 01111110 1
00010010 10100101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00111110 01111111 011110001 00001100 0
00000011 10010111 1
00011001 10110000 1
01010001 00010100 1
00000100 01000010 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:
10110000 00000100 0
01011001 01100100 1
01001100 01101111 1
01010000 10101001 0
10100010 00000011 1
01010111 10100101 1
1. The parity bits for the 16 columns is: 01010111 10100101
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 (0,1):
10001010 00001110 0
10101100 11111011 0
00110011 10100111 1
01111010 10001001 0
11111101 01111110 1
00010010 10100101 0
For figure 3, the bits that were flipped are (0,3) and (14,1):
00111110 01111111 0
11110001 00001100 0
00000011 10010111 1
00011001 10110000 1
01010001 00010100 1
00000100 01000010 1
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 0101011110100101
The answer was: 01101
The answer was: 1
The answer was: 0,1
The answer was: No