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 111100110 10100011
11110101 00011100
00000100 10010100
10100000 00100101
01010101 11100100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11011111 00111111 001110011 00110100 0
00010111 00101100 1
01111110 01100101 0
10011100 01010110 0
01011101 00010100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11001000 01101000 000010101 10100000 1
01110001 00010011 0
01101111 00110101 0
00111010 11010001 0
11101001 00111111 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:
11100110 10100011 1
11110101 00011100 1
00000100 10010100 0
10100000 00100101 1
01010101 11100100 0
11100010 11101010 1
1. The parity bits for the 16 columns is: 11100010 11101010
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (5,0):
11011111 00111111 0
01110011 00110100 0
00010111 00101100 1
01111110 01100101 0
10011100 01010110 0
01011101 00010100 1
For figure 3, the bit that was flipped is (3,2):
11001000 01101000 0
00010101 10100000 1
01110001 00010011 0
01101111 00110101 0
00111010 11010001 0
11101001 00111111 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: 1110001011101010
The answer was: 11010
The answer was: 1
The answer was: 5,0
The answer was: Yes