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 111001110 01011000
10110110 01011010
10011000 00110111
01110100 11100101
00100101 10000010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11101111 01001000 110000101 01001001 1
10110100 11100111 0
01100011 00100001 0
10000111 00011110 0
00111010 11011011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000010 11011111 110100000 01010101 0
00010000 00101010 0
01110011 01010101 1
00111001 11001000 1
01111000 00011101 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:
11001110 01011000 0
10110110 01011010 1
10011000 00110111 0
01110100 11100101 1
00100101 10000010 1
10110001 01010010 1
1. The parity bits for the 16 columns is: 10110001 01010010
2. The parity bits for the 5 rows is: 01011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (14,1):
11101111 01001000 1
10000101 01001001 1
10110100 11100111 0
01100011 00100001 0
10000111 00011110 0
00111010 11011011 0
For figure 3, the bit that was flipped is (10,5):
10000010 11011111 1
10100000 01010101 0
00010000 00101010 0
01110011 01010101 1
00111001 11001000 1
01111000 00011101 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: 1011000101010010
The answer was: 01011
The answer was: 1
The answer was: 14,1
The answer was: Yes