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 111111110 10110000
00111001 00111010
00000011 10010101
11011000 11111101
00011000 10000110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11011011 01111001 111101001 00100010 1
10001111 00101001 0
01101011 01100110 1
00010110 01111010 1
01000000 01101110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10101110 11100101 010010101 10010011 0
01011111 11010111 1
00101101 00100101 1
00100111 01111111 0
00101111 11111011 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:
11111110 10110000 0
00111001 00111010 0
00000011 10010101 0
11011000 11111101 1
00011000 10000110 1
00000100 01100100 0
1. The parity bits for the 16 columns is: 00000100 01100100
2. The parity bits for the 5 rows is: 00011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (0,4):
11011011 01111001 1
11101001 00100010 1
10001111 00101001 0
01101011 01100110 1
00010110 01111010 1
01000000 01101110 0
For figure 3, the bits that were flipped are (1,2) and (7,4):
10101110 11100101 0
10010101 10010011 0
01011111 11010111 1
00101101 00100101 1
00100111 01111111 0
00101111 11111011 0
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: 0000010001100100
The answer was: 00011
The answer was: 0
The answer was: 0,4
The answer was: No