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 101001011 10110000
10111000 01001111
10010101 10010100
11111100 01101111
10111011 10001011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00001000 01110011 100111110 01010111 0
01000110 11111110 0
10100000 01111001 1
11111101 11101101 1
00101101 01011110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100011 11101100 111111010 01110111 1
00110101 01010101 0
00011100 11100011 0
10001110 10011001 0
01111110 10110100 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:
01001011 10110000 1
10111000 01001111 1
10010101 10010100 1
11111100 01101111 0
10111011 10001011 0
00100001 10001111 1
1. The parity bits for the 16 columns is: 00100001 10001111
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 (11,0):
00001000 01110011 1
00111110 01010111 0
01000110 11111110 0
10100000 01111001 1
11111101 11101101 1
00101101 01011110 1
For figure 3, the bit that was flipped is (1,1):
01100011 11101100 1
11111010 01110111 1
00110101 01010101 0
00011100 11100011 0
10001110 10011001 0
01111110 10110100 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: 0010000110001111
The answer was: 11100
The answer was: 1
The answer was: 11,0
The answer was: Yes