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 100001110 00010111
11011011 11011011
10011011 11001011
00001010 01101111
10101000 00000010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10101110 01010001 101001101 11110001 1
00011111 01100100 0
10111101 01111011 0
01011101 00000111 0
00010100 10111000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11111110 01010010 000110000 00100110 0
10111111 10010101 1
10001011 10111100 1
00110101 11100010 0
11001111 10111011 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:
00001110 00010111 1
11011011 11011011 0
10011011 11001011 0
00001010 01101111 0
10101000 00000010 0
11101100 01101010 1
1. The parity bits for the 16 columns is: 11101100 01101010
2. The parity bits for the 5 rows is: 10000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (4,0):
10101110 01010001 1
01001101 11110001 1
00011111 01100100 0
10111101 01111011 0
01011101 00000111 0
00010100 10111000 0
For figure 3, the bit that was flipped is (13,1):
11111110 01010010 0
00110000 00100110 0
10111111 10010101 1
10001011 10111100 1
00110101 11100010 0
11001111 10111011 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: 1110110001101010
The answer was: 10000
The answer was: 1
The answer was: 4,0
The answer was: Yes