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 100011101 10101010
10011001 11111100
10011011 11110111
01011010 01010000
10101100 00001001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101100 10101110 010000010 10000101 0
10001101 10100111 1
10100111 10001000 1
00110000 11110111 1
10110100 11110011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000101 01110101 110000010 01000110 1
01010100 01011000 1
01000010 01001001 1
01010111 00111000 0
01000110 00011010 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:
00011101 10101010 0
10011001 11111100 0
10011011 11110111 0
01011010 01010000 0
10101100 00001001 0
11101001 11111000 0
1. The parity bits for the 16 columns is: 11101001 11111000
2. The parity bits for the 5 rows is: 00000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,1):
00101100 10101110 0
10000010 10000101 0
10001101 10100111 1
10100111 10001000 1
00110000 11110111 1
10110100 11110011 0
For figure 3, the bit that was flipped is (1,2):
11000101 01110101 1
10000010 01000110 1
01010100 01011000 1
01000010 01001001 1
01010111 00111000 0
01000110 00011010 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: 1110100111111000
The answer was: 00000
The answer was: 0
The answer was: 16,1
The answer was: Yes