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 111011101 11011110
01000000 10010100
00110001 11101110
10111111 00001010
01111010 01110011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01000100 10100100 110111101 00011000 0
11100000 00001011 0
01000111 11010010 0
10001001 10010100 1
11010111 11110011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100001 01100001 011101100 10111010 0
10011110 01110010 1
11000000 01010110 0
10000001 00100001 1
10010110 11011110 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:
11011101 11011110 0
01000000 10010100 0
00110001 11101110 1
10111111 00001010 1
01111010 01110011 0
01101001 11011101 0
1. The parity bits for the 16 columns is: 01101001 11011101
2. The parity bits for the 5 rows is: 00110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,4):
01000100 10100100 1
10111101 00011000 0
11100000 00001011 0
01000111 11010010 0
10001001 10010100 1
11010111 11110011 0
For figure 3, the bit that was flipped is (5,4):
10100001 01100001 0
11101100 10111010 0
10011110 01110010 1
11000000 01010110 0
10000001 00100001 1
10010110 11011110 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0110100111011101
The answer was: 00110
The answer was: 0
The answer was: 14,4
The answer was: Yes