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 111101001 00111100
10101110 10110111
10001010 00000110
00101110 00001111
00001011 00011010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00110000 00110111 100000001 00100110 0
11100100 10101001 1
10011011 10111100 0
00100100 11100100 0
01101000 11100000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01111001 10100111 101111111 11101110 1
01001011 11111101 1
01111111 10111101 1
11001001 10010111 1
11111001 10011110 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:
11101001 00111100 1
10101110 10110111 1
10001010 00000110 1
00101110 00001111 0
00001011 00011010 0
11101000 10011000 1
1. The parity bits for the 16 columns is: 11101000 10011000
2. The parity bits for the 5 rows is: 11100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (6,2):
00110000 00110111 1
00000001 00100110 0
11100100 10101001 1
10011011 10111100 0
00100100 11100100 0
01101000 11100000 0
For figure 3, the bit that was flipped is (6,0):
01111001 10100111 1
01111111 11101110 1
01001011 11111101 1
01111111 10111101 1
11001001 10010111 1
11111001 10011110 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: 1110100010011000
The answer was: 11100
The answer was: 1
The answer was: 6,2
The answer was: Yes