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 100001001 10001001
11000000 10111011
00011011 00100000
10101100 00101101
10100001 10111110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00110101 01100010 101100100 10111101 0
00001000 10010001 0
01111011 00010000 1
01101010 11001101 1
00001000 10010011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000101 10001111 010111001 01000110 0
01110000 10101000 1
10101110 00010111 1
00011011 01110000 1
00111001 01000110 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:
00001001 10001001 1
11000000 10111011 0
00011011 00100000 1
10101100 00101101 0
10100001 10111110 1
11011111 10000001 1
1. The parity bits for the 16 columns is: 11011111 10000001
2. The parity bits for the 5 rows is: 10101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (1,1):
00110101 01100010 1
01100100 10111101 0
00001000 10010001 0
01111011 00010000 1
01101010 11001101 1
00001000 10010011 1
For figure 3, the bit that was flipped is (9,2):
01000101 10001111 0
10111001 01000110 0
01110000 10101000 1
10101110 00010111 1
00011011 01110000 1
00111001 01000110 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: 1101111110000001
The answer was: 10101
The answer was: 1
The answer was: 1,1
The answer was: Yes