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 101000010 00101010
00110010 00011011
10011110 10110011
11011000 01000101
01000111 10101101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111001 01001101 100110101 10010101 0
10011101 01100000 1
11101111 01010111 0
11101101 00000100 1
01010011 11101011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01001110 10000000 110000011 11110000 0
00100100 10011110 1
10111010 00110111 0
11011110 01011110 1
10001101 10010111 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:
01000010 00101010 1
00110010 00011011 1
10011110 10110011 0
11011000 01000101 1
01000111 10101101 1
01110001 01101010 0
1. The parity bits for the 16 columns is: 01110001 01101010
2. The parity bits for the 5 rows is: 11011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,0):
11111001 01001101 1
00110101 10010101 0
10011101 01100000 1
11101111 01010111 0
11101101 00000100 1
01010011 11101011 0
For figure 3, the bit that was flipped is (11,1):
01001110 10000000 1
10000011 11110000 0
00100100 10011110 1
10111010 00110111 0
11011110 01011110 1
10001101 10010111 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: 0111000101101010
The answer was: 11011
The answer was: 0
The answer was: 16,0
The answer was: Yes