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 101100111 01000010
11111101 01011100
01000111 10101111
00011010 11010100
11011010 01111000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011000 11110100 110011001 11101011 0
01101101 01101101 1
00000111 00001001 1
01010000 00101000 0
10111111 01010011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011000 01001000 000101101 01000001 0
00100001 00001100 1
00001011 10001000 1
00010111 01001111 1
00011000 11000010 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:
01100111 01000010 1
11111101 01011100 1
01000111 10101111 0
00011010 11010100 1
11011010 01111000 1
00011101 00011101 0
1. The parity bits for the 16 columns is: 00011101 00011101
2. The parity bits for the 5 rows is: 11011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (5,2):
00011000 11110100 1
10011001 11101011 0
01101101 01101101 1
00000111 00001001 1
01010000 00101000 0
10111111 01010011 1
For figure 3, the bit that was flipped is (3,2):
00011000 01001000 0
00101101 01000001 0
00100001 00001100 1
00001011 10001000 1
00010111 01001111 1
00011000 11000010 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: 0001110100011101
The answer was: 11011
The answer was: 0
The answer was: 5,2
The answer was: Yes