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 111011111 10101100
10000011 00011111
01010010 11100100
01111110 11000001
11101001 00111101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11001000 00110100 000001011 00001000 0
11010111 11111000 1
00010001 01101100 0
01010100 11110100 0
00010001 01011100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10010101 01010100 100001111 11000110 0
00100011 01100101 1
10010110 10100011 0
00001110 00011101 0
00100101 01001001 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:
11011111 10101100 1
10000011 00011111 0
01010010 11100100 1
01111110 11000001 1
11101001 00111101 0
10011001 10101011 1
1. The parity bits for the 16 columns is: 10011001 10101011
2. The parity bits for the 5 rows is: 10110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (1,5):
11001000 00110100 0
00001011 00001000 0
11010111 11111000 1
00010001 01101100 0
01010100 11110100 0
00010001 01011100 1
For figure 3, the bit that was flipped is (5,4):
10010101 01010100 1
00001111 11000110 0
00100011 01100101 1
10010110 10100011 0
00001110 00011101 0
00100101 01001001 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: 1001100110101011
The answer was: 10110
The answer was: 1
The answer was: 1,5
The answer was: Yes