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 110010001 00101110
10101111 10001101
01110001 11011000
11110100 11101001
11110000 11101010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11101010 01011100 111011011 01110101 1
10100001 01100000 1
01110101 11100010 1
11011010 11101011 0
00111111 01000001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101011 01001011 010100110 00001110 1
01011000 11000101 0
00100000 00101111 0
10000010 10100011 0
01110111 00001101 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:
10010001 00101110 1
10101111 10001101 0
01110001 11011000 0
11110100 11101001 0
11110000 11101010 1
01001011 01111000 0
1. The parity bits for the 16 columns is: 01001011 01111000
2. The parity bits for the 5 rows is: 10001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (15,4):
11101010 01011100 1
11011011 01110101 1
10100001 01100000 1
01110101 11100010 1
11011010 11101011 0
00111111 01000001 0
For figure 3, the bit that was flipped is (15,2):
00101011 01001011 0
10100110 00001110 1
01011000 11000101 0
00100000 00101111 0
10000010 10100011 0
01110111 00001101 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: 0100101101111000
The answer was: 10001
The answer was: 0
The answer was: 15,4
The answer was: Yes