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 101010101 10110010
01100101 01000011
01100010 01000011
10000110 00111110
11000000 00101110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10100001 11101000 100000110 10100010 1
01011000 10001111 0
11100010 00001101 1
00010101 00001101 1
00000000 11000101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101100 11101101 100100010 10001001 0
00110010 10001000 1
01111100 01000000 0
00100110 01011001 1
10100111 11110101 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:
01010101 10110010 0
01100101 01000011 1
01100010 01000011 0
10000110 00111110 0
11000000 00101110 0
00010100 10100010 1
1. The parity bits for the 16 columns is: 00010100 10100010
2. The parity bits for the 5 rows is: 01000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (4,4):
10100001 11101000 1
00000110 10100010 1
01011000 10001111 0
11100010 00001101 1
00010101 00001101 1
00000000 11000101 0
For figure 3, the bit that was flipped is (7,1):
11101100 11101101 1
00100010 10001001 0
00110010 10001000 1
01111100 01000000 0
00100110 01011001 1
10100111 11110101 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: 0001010010100010
The answer was: 01000
The answer was: 1
The answer was: 4,4
The answer was: Yes