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 111001011 01100001
10100101 00000110
11101110 10001111
11100001 10100010
01010101 10010010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11100100 11010010 011000010 11111010 1
00111010 01000011 1
10110000 00111110 0
11010001 01011111 1
01111101 00001011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01101110 01001001 010011011 00010011 0
01000111 10100010 1
10100110 00010100 1
11111011 11001111 1
11101111 00110011 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:
11001011 01100001 0
10100101 00000110 0
11101110 10001111 1
11100001 10100010 1
01010101 10010010 1
00110100 11011000 1
1. The parity bits for the 16 columns is: 00110100 11011000
2. The parity bits for the 5 rows is: 00111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (15,4):
11100100 11010010 0
11000010 11111010 1
00111010 01000011 1
10110000 00111110 0
11010001 01011111 1
01111101 00001011 1
For figure 3, the bit that was flipped is (11,3):
01101110 01001001 0
10011011 00010011 0
01000111 10100010 1
10100110 00010100 1
11111011 11001111 1
11101111 00110011 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: 0011010011011000
The answer was: 00111
The answer was: 1
The answer was: 15,4
The answer was: Yes