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 111010100 01011101
01100010 10111000
00100010 00101101
00110000 00100011
10100111 10110000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01010101 00011001 110100001 00101111 0
01011010 10001100 0
01101100 10000110 1
00100001 11000111 1
11100111 11111011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10011000 11111111 100110101 10011101 1
10110000 11011100 1
01011111 10110111 0
00001010 00000010 1
01001000 00101011 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:
11010100 01011101 1
01100010 10111000 1
00100010 00101101 0
00110000 00100011 1
10100111 10110000 0
00000011 01011011 1
1. The parity bits for the 16 columns is: 00000011 01011011
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (5,2):
01010101 00011001 1
10100001 00101111 0
01011010 10001100 0
01101100 10000110 1
00100001 11000111 1
11100111 11111011 1
For figure 3, the bit that was flipped is (10,2):
10011000 11111111 1
00110101 10011101 1
10110000 11011100 1
01011111 10110111 0
00001010 00000010 1
01001000 00101011 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: 0000001101011011
The answer was: 11010
The answer was: 1
The answer was: 5,2
The answer was: Yes