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 101011111 01011100
01110010 00111100
00011101 10111101
01100001 11111010
00001001 00111001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10100110 01110001 000101111 11111001 0
11010111 01111100 1
00000010 01111001 0
00110100 10100010 0
01101001 00101111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011100 01100001 010111011 10101111 0
01001101 00000001 1
01001110 10110000 0
10011101 01111000 1
00101001 00000111 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:
01011111 01011100 0
01110010 00111100 0
00011101 10111101 0
01100001 11111010 1
00001001 00111001 0
01011000 00011110 1
1. The parity bits for the 16 columns is: 01011000 00011110
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 (7,1):
10100110 01110001 0
00101111 11111001 0
11010111 01111100 1
00000010 01111001 0
00110100 10100010 0
01101001 00101111 1
For figure 3, the bit that was flipped is (3,3):
00011100 01100001 0
10111011 10101111 0
01001101 00000001 1
01001110 10110000 0
10011101 01111000 1
00101001 00000111 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0101100000011110
The answer was: 00010
The answer was: 1
The answer was: 7,1
The answer was: Yes