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 101011100 00011101
10001010 11010010
00011010 00011011
11110110 00110000
00110000 10100010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11011010 00110000 110100010 10100001 0
01100101 01001000 0
00101011 11111010 0
00111010 01100010 1
00000100 01000001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11100001 00000010 001000001 10110111 0
10110111 11010000 1
00001111 10011000 1
11000101 01111110 0
11011101 11000011 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:
01011100 00011101 0
10001010 11010010 1
00011010 00011011 1
11110110 00110000 0
00110000 10100010 1
00001010 01000110 1
1. The parity bits for the 16 columns is: 00001010 01000110
2. The parity bits for the 5 rows is: 01101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (4,5):
11011010 00110000 1
10100010 10100001 0
01100101 01001000 0
00101011 11111010 0
00111010 01100010 1
00000100 01000001 0
For figure 3, the bit that was flipped is (9,0):
11100001 00000010 0
01000001 10110111 0
10110111 11010000 1
00001111 10011000 1
11000101 01111110 0
11011101 11000011 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: 0000101001000110
The answer was: 01101
The answer was: 1
The answer was: 4,5
The answer was: Yes