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 111110000 10000010
01110010 00111000
11100011 10000111
00111111 10000110
10111010 11110110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00111111 10110001 101001110 00001001 0
10101100 11011011 0
00011010 01010010 0
00010000 01000111 1
11110111 01110110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01111011 10000111 101100000 11010111 0
01011000 00100010 1
01001011 01001000 0
01111100 11100100 1
01110101 11011110 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:
11110000 10000010 0
01110010 00111000 1
11100011 10000111 1
00111111 10000110 1
10111010 11110110 1
11100100 01001101 0
1. The parity bits for the 16 columns is: 11100100 01001101
2. The parity bits for the 5 rows is: 01111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (2,0):
00111111 10110001 1
01001110 00001001 0
10101100 11011011 0
00011010 01010010 0
00010000 01000111 1
11110111 01110110 0
For figure 3, the bit that was flipped is (7,0):
01111011 10000111 1
01100000 11010111 0
01011000 00100010 1
01001011 01001000 0
01111100 11100100 1
01110101 11011110 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: 1110010001001101
The answer was: 01111
The answer was: 0
The answer was: 2,0
The answer was: Yes