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 110111111 01101111
01010000 11010101
01011001 00000111
11110001 10001100
00000000 10000110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00111111 10001011 001110000 00111100 1
00110001 00101100 0
00000111 00111001 1
10100100 01111110 0
11011101 11011000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00100010 01001110 011000100 10110100 0
11000010 10111010 0
11101101 11111001 0
00001100 01011101 1
11000100 11100100 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:
10111111 01101111 1
01010000 11010101 1
01011001 00000111 1
11110001 10001100 0
00000000 10000110 1
01000111 10110111 0
1. The parity bits for the 16 columns is: 01000111 10110111
2. The parity bits for the 5 rows is: 11101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (13,4):
00111111 10001011 0
01110000 00111100 1
00110001 00101100 0
00000111 00111001 1
10100100 01111110 0
11011101 11011000 0
For figure 3, the bit that was flipped is (7,1):
00100010 01001110 0
11000100 10110100 0
11000010 10111010 0
11101101 11111001 0
00001100 01011101 1
11000100 11100100 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: 0100011110110111
The answer was: 11101
The answer was: 0
The answer was: 13,4
The answer was: Yes