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 111001111 01110010
11110111 11111010
00001000 00100000
00011000 01000000
11110101 11011011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011000 01011110 011111000 11100011 0
10010000 11110101 0
00110101 11101001 0
00101011 01010010 1
11101111 11110011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01111110 11001000 100111000 00001111 0
01100011 00111111 0
11100010 11101110 0
10011010 10000000 1
01111101 10010110 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:
11001111 01110010 0
11110111 11111010 1
00001000 00100000 0
00011000 01000000 1
11110101 11011011 0
11011101 00110011 0
1. The parity bits for the 16 columns is: 11011101 00110011
2. The parity bits for the 5 rows is: 01010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (7,3):
10011000 01011110 0
11111000 11100011 0
10010000 11110101 0
00110101 11101001 0
00101011 01010010 1
11101111 11110011 1
For figure 3, the bit that was flipped is (2,1):
01111110 11001000 1
00111000 00001111 0
01100011 00111111 0
11100010 11101110 0
10011010 10000000 1
01111101 10010110 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: 1101110100110011
The answer was: 01010
The answer was: 0
The answer was: 7,3
The answer was: Yes