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 101011110 01111000
00111111 10010111
10100110 00110100
01010111 10110001
11001001 11010010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101111 01000111 100111100 10101110 1
10001110 10010001 0
01000100 11101110 0
00010010 00110100 1
11001011 10100110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10110110 00010011 011011000 00111010 0
10011011 00011101 0
10110100 10110010 0
01110100 00100010 0
00110101 10000100 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:
01011110 01111000 1
00111111 10010111 1
10100110 00110100 1
01010111 10110001 1
11001001 11010010 0
01011001 10111000 0
1. The parity bits for the 16 columns is: 01011001 10111000
2. The parity bits for the 5 rows is: 11110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (13,2):
00101111 01000111 1
00111100 10101110 1
10001110 10010001 0
01000100 11101110 0
00010010 00110100 1
11001011 10100110 1
For figure 3, the bit that was flipped is (10,2):
10110110 00010011 0
11011000 00111010 0
10011011 00011101 0
10110100 10110010 0
01110100 00100010 0
00110101 10000100 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: 0101100110111000
The answer was: 11110
The answer was: 0
The answer was: 13,2
The answer was: Yes