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 111100100 00011111
10011111 10010100
00011111 01100000
10001011 00110000
01001111 11111111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110100 01001000 100001000 01101100 1
11101101 00100011 0
00110000 11001000 1
01100100 00001010 1
01000111 11000101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11110011 10101101 100001101 01000001 1
10100101 01001100 1
10010110 10011000 0
00000000 01110110 1
11001101 11001110 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:
11100100 00011111 1
10011111 10010100 1
00011111 01100000 1
10001011 00110000 0
01001111 11111111 1
10100000 00100100 0
1. The parity bits for the 16 columns is: 10100000 00100100
2. The parity bits for the 5 rows is: 11101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (6,2):
11110100 01001000 1
00001000 01101100 1
11101101 00100011 0
00110000 11001000 1
01100100 00001010 1
01000111 11000101 0
For figure 3, the bit that was flipped is (8,3):
11110011 10101101 1
00001101 01000001 1
10100101 01001100 1
10010110 10011000 0
00000000 01110110 1
11001101 11001110 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: 1010000000100100
The answer was: 11101
The answer was: 0
The answer was: 6,2
The answer was: Yes