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 110101100 01011000
11101110 11101111
00100110 11011011
11001111 00000000
01100110 01110101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101100 01011001 010001110 01100011 0
11000101 11101001 1
11010000 01010111 0
00001111 01010100 1
11111000 11010000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00111000 11111010 100110010 10000100 1
00011101 11010000 1
01100101 11000001 0
10010101 10110011 1
11100111 10011100 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:
10101100 01011000 1
11101110 11101111 1
00100110 11011011 1
11001111 00000000 0
01100110 01110101 1
11001101 00011001 0
1. The parity bits for the 16 columns is: 11001101 00011001
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 (1,0):
00101100 01011001 0
10001110 01100011 0
11000101 11101001 1
11010000 01010111 0
00001111 01010100 1
11111000 11010000 0
For figure 3, the bit that was flipped is (9,3):
00111000 11111010 1
00110010 10000100 1
00011101 11010000 1
01100101 11000001 0
10010101 10110011 1
11100111 10011100 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: 1100110100011001
The answer was: 11101
The answer was: 0
The answer was: 1,0
The answer was: Yes