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 101101000 10001001
00110000 11000111
11011001 00001100
01000101 00111000
01100010 10010000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11101000 01000001 010111011 00111011 0
10001111 01100111 0
10010111 11111110 0
11100101 11001011 0
10101110 00101100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011101 01000011 111110010 01101111 1
01010101 10110000 0
11011110 10100001 1
10000100 10101111 0
00100000 10010010 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:
01101000 10001001 0
00110000 11000111 1
11011001 00001100 1
01000101 00111000 0
01100010 10010000 1
10100110 11101010 1
1. The parity bits for the 16 columns is: 10100110 11101010
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 (13,1):
11101000 01000001 0
10111011 00111011 0
10001111 01100111 0
10010111 11111110 0
11100101 11001011 0
10101110 00101100 0
For figure 3, the bit that was flipped is (16,2):
11011101 01000011 1
11110010 01101111 1
01010101 10110000 0
11011110 10100001 1
10000100 10101111 0
00100000 10010010 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: 1010011011101010
The answer was: 01101
The answer was: 1
The answer was: 13,1
The answer was: Yes