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 100110010 11000101
00010111 11010111
11100110 11110011
01011110 01111001
00111001 00111100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010001 01000001 101001001 11101111 0
10000100 01101101 0
00100111 10111111 1
11101101 10000111 0
10010110 01111011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000111 11000110 011111111 01110111 0
01000011 01001101 0
01110110 10011000 0
01010010 01000010 1
11011111 00100111 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:
00110010 11000101 1
00010111 11010111 0
11100110 11110011 1
01011110 01111001 0
00111001 00111100 0
10100100 10100100 0
1. The parity bits for the 16 columns is: 10100100 10100100
2. The parity bits for the 5 rows is: 10100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (8,2):
10010001 01000001 1
01001001 11101111 0
10000100 01101101 0
00100111 10111111 1
11101101 10000111 0
10010110 01111011 0
For figure 3, the bit that was flipped is (15,2):
01000111 11000110 0
11111111 01110111 0
01000011 01001101 0
01110110 10011000 0
01010010 01000010 1
11011111 00100111 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: 1010010010100100
The answer was: 10100
The answer was: 0
The answer was: 8,2
The answer was: Yes