### 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 1*

11101001 01100110

00010001 10000100

00010100 00010111

01000011 10111010

11001000 10010011

*Figure 2*

Both the payload and parity bits are shown. One of these bits is flipped.

00000110 01010111 110001000 01000101 1

11110010 11101011 1

01111111 01000011 0

01011010 10110110 1

01011001 00101100 0

*Figure 3*

Both the payload and parity bits are shown; Either one or two of the bits have been flipped.

10000001 11010111 001000110 00000110 0

10011100 00101110 0

00110001 01111010 0

00100000 00001011 1

01011011 10001110 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:

11101001 01100110 1

00010001 10000100 0

00010100 00010111 0

01000011 10111010 0

11001000 10010011 1

01100111 11011100 0

1. The parity bits for the 16 columns is: 01100111 11011100

2. The parity bits for the 5 rows is: 10001

3. The parity bit for the parity row is: 0

4. The bit that was flipped in figure 2 is (10,5):

00000110 01010111 1

10001000 01000101 1

11110010 11101011 1

01111111 01000011 0

01011010 10110110 1

01011001 00101100 0

For figure 3, the bits that were flipped are (7,1) and (3,4):

10000001 11010111 0

01000110 00000110 0

10011100 00101110 0

00110001 01111010 0

00100000 00001011 1

01011011 10001110 1

5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.

That's incorrect

That's correct

The answer was: 0110011111011100

The answer was: 10001

The answer was: 0

The answer was: 10,5

The answer was: No