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 101100110 00101111
01010011 00111010
01000110 00010111
11011101 11111010
11011010 10111001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011100 00011111 001001011 10111001 1
10100111 10100011 1
11010010 10110001 0
11100001 00100000 0
11000011 10010110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100100 11110011 101011000 10100011 1
00001000 11101110 1
00010011 00000111 1
00011001 01100101 1
00111110 11011101 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:
01100110 00101111 1
01010011 00111010 0
01000110 00010111 1
11011101 11111010 0
11011010 10111001 0
01110100 01000001 0
1. The parity bits for the 16 columns is: 01110100 01000001
2. The parity bits for the 5 rows is: 10100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,4):
00011100 00011111 0
01001011 10111001 1
10100111 10100011 1
11010010 10110001 0
11100001 00100000 0
11000011 10010110 0
For figure 3, the bit that was flipped is (15,3):
01100100 11110011 1
01011000 10100011 1
00001000 11101110 1
00010011 00000111 1
00011001 01100101 1
00111110 11011101 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: 0111010001000001
The answer was: 10100
The answer was: 0
The answer was: 14,4
The answer was: Yes