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 111101111 00110010
00110111 10000011
00000101 10111111
00011110 00111100
10100000 10001111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01011110 00011110 111100100 10010110 0
10111010 10010101 1
11101100 11101101 1
10001111 11011011 1
01100011 00101011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00110110 01001000 010011100 11110010 0
00100100 00011010 1
00011000 10010011 0
00111001 00101011 0
10001111 00011000 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:
11101111 00110010 0
00110111 10000011 0
00000101 10111111 1
00011110 00111100 0
10100000 10001111 1
01100011 10111101 0
1. The parity bits for the 16 columns is: 01100011 10111101
2. The parity bits for the 5 rows is: 00101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,5):
01011110 00011110 1
11100100 10010110 0
10111010 10010101 1
11101100 11101101 1
10001111 11011011 1
01100011 00101011 1
For figure 3, the bit that was flipped is (2,1):
00110110 01001000 0
10011100 11110010 0
00100100 00011010 1
00011000 10010011 0
00111001 00101011 0
10001111 00011000 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: 0110001110111101
The answer was: 00101
The answer was: 0
The answer was: 16,5
The answer was: Yes