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 111100100 01001011
10011010 11101000
00011011 00101110
00000001 11001000
00101000 11010010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01000111 11011010 110111110 00101100 1
10011111 10011111 0
01000000 10001100 1
01110110 00110000 1
01010000 11010001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100111 11110101 110100111 10101100 1
01000100 01111100 1
01000100 00111110 1
11110101 11101010 0
11110111 11110001 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:
11100100 01001011 0
10011010 11101000 0
00011011 00101110 0
00000001 11001000 0
00101000 11010010 0
01001100 10010111 0
1. The parity bits for the 16 columns is: 01001100 10010111
2. The parity bits for the 5 rows is: 00000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (13,3):
01000111 11011010 1
10111110 00101100 1
10011111 10011111 0
01000000 10001100 1
01110110 00110000 1
01010000 11010001 0
For figure 3, the bit that was flipped is (6,4):
10100111 11110101 1
10100111 10101100 1
01000100 01111100 1
01000100 00111110 1
11110101 11101010 0
11110111 11110001 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: 0100110010010111
The answer was: 00000
The answer was: 0
The answer was: 13,3
The answer was: Yes