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 101111011 11011011
00110001 11011100
00100000 11000111
11000010 11001100
11100110 11110100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11100000 10100111 010100111 10100110 1
10011110 00000001 0
11010100 01001100 1
00001011 10100000 0
00000110 11001100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100001 00000010 100010100 00011000 0
00100100 01110110 1
11110000 01101111 0
00101010 10110100 1
01001011 10110110 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:
01111011 11011011 0
00110001 11011100 0
00100000 11000111 0
11000010 11001100 1
11100110 11110100 0
01001110 11111000 1
1. The parity bits for the 16 columns is: 01001110 11111000
2. The parity bits for the 5 rows is: 00010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (10,4):
11100000 10100111 0
10100111 10100110 1
10011110 00000001 0
11010100 01001100 1
00001011 10100000 0
00000110 11001100 0
For figure 3, the bit that was flipped is (15,0):
10100001 00000010 1
00010100 00011000 0
00100100 01110110 1
11110000 01101111 0
00101010 10110100 1
01001011 10110110 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: 0100111011111000
The answer was: 00010
The answer was: 1
The answer was: 10,4
The answer was: Yes