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 111000000 00101101
10010010 01000010
00001100 00001110
10110101 11001011
00111111 10110100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01000100 11111111 111101100 01001111 0
00101001 10001111 0
10001111 10110110 0
11110100 11011000 1
11111010 01000001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000001 01100011 011001101 00100010 1
11011110 01000000 1
01110101 11000111 0
01110011 10001111 1
10010110 01001001 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:
11000000 00101101 0
10010010 01000010 1
00001100 00001110 1
10110101 11001011 0
00111111 10110100 0
11010100 00011110 0
1. The parity bits for the 16 columns is: 11010100 00011110
2. The parity bits for the 5 rows is: 01100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,0):
01000100 11111111 1
11101100 01001111 0
00101001 10001111 0
10001111 10110110 0
11110100 11011000 1
11111010 01000001 0
For figure 3, the bit that was flipped is (6,4):
10000001 01100011 0
11001101 00100010 1
11011110 01000000 1
01110101 11000111 0
01110011 10001111 1
10010110 01001001 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: 1101010000011110
The answer was: 01100
The answer was: 0
The answer was: 11,0
The answer was: Yes