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 110110111 11000110
10111111 10010101
00110010 01011011
01010000 11110011
01101100 00011111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101101 01111011 010000101 00101001 0
01001010 11010101 0
00111010 00100010 1
10000011 11100100 1
01001011 01000001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101111 11101000 111000100 11111010 1
01000111 11110100 0
11111011 00111001 1
10011001 00000111 1
01001110 11011000 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:
10110111 11000110 0
10111111 10010101 1
00110010 01011011 0
01010000 11110011 0
01101100 00011111 1
00000110 11100100 0
1. The parity bits for the 16 columns is: 00000110 11100100
2. The parity bits for the 5 rows is: 01001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,3):
00101101 01111011 0
10000101 00101001 0
01001010 11010101 0
00111010 00100010 1
10000011 11100100 1
01001011 01000001 0
For figure 3, the bit that was flipped is (0,2):
00101111 11101000 1
11000100 11111010 1
01000111 11110100 0
11111011 00111001 1
10011001 00000111 1
01001110 11011000 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: 0000011011100100
The answer was: 01001
The answer was: 0
The answer was: 3,3
The answer was: Yes