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 110111010 01000010
01010001 10001011
11101001 01110100
01101110 00001110
00101001 10100001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11000000 01010100 000010111 00101111 1
10010110 01100111 1
01110001 00110011 0
11111111 10011000 1
11001111 10110011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110100 10101111 011100110 01101100 0
11111001 00101111 1
11110010 11011111 1
10101011 11001011 0
10110010 11111010 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:
10111010 01000010 1
01010001 10001011 1
11101001 01110100 1
01101110 00001110 0
00101001 10100001 0
01000101 00010010 1
1. The parity bits for the 16 columns is: 01000101 00010010
2. The parity bits for the 5 rows is: 11100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,0):
11000000 01010100 0
00010111 00101111 1
10010110 01100111 1
01110001 00110011 0
11111111 10011000 1
11001111 10110011 1
For figure 3, the bits that were flipped are (14,1) and (0,3):
01110100 10101111 0
11100110 01101100 0
11111001 00101111 1
11110010 11011111 1
10101011 11001011 0
10110010 11111010 0
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 0100010100010010
The answer was: 11100
The answer was: 1
The answer was: 13,0
The answer was: No