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 111000010 00001011
00100100 11001111
10011111 00010011
01010010 00100010
10010111 11010001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00010000 10111010 011111010 10111011 1
00010000 10101000 0
11111010 00000000 0
00110011 11101011 0
00110011 11000010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100010 00111110 011000100 00100001 1
11101110 10000011 0
10100001 10001010 0
10110011 00110010 0
01011010 00100101 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:
11000010 00001011 0
00100100 11001111 0
10011111 00010011 1
01010010 00100010 1
10010111 11010001 1
10111100 00100100 1
1. The parity bits for the 16 columns is: 10111100 00100100
2. The parity bits for the 5 rows is: 00111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (8,1):
00010000 10111010 0
11111010 10111011 1
00010000 10101000 0
11111010 00000000 0
00110011 11101011 0
00110011 11000010 1
For figure 3, the bit that was flipped is (15,2):
01100010 00111110 0
11000100 00100001 1
11101110 10000011 0
10100001 10001010 0
10110011 00110010 0
01011010 00100101 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: 1011110000100100
The answer was: 00111
The answer was: 1
The answer was: 8,1
The answer was: Yes