### 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*

01100010 11000011

01110100 11101111

01010111 01101010

01010011 01000101

01011000 11000110

*Figure 2*

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

11001101 00001101 110010010 00111000 0

00111001 00001110 1

10101100 10101110 1

01101101 00100011 0

10100101 10110110 1

*Figure 3*

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

11110100 00101101 111001100 01110011 0

11101111 10110111 1

10011001 10111011 0

10111110 01010111 1

11110000 00000111 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:

01100010 11000011 1

01110100 11101111 1

01010111 01101010 1

01010011 01000101 1

01011000 11000110 1

01001010 11000101 1

1. The parity bits for the 16 columns is: 01001010 11000101

2. The parity bits for the 5 rows is: 11111

3. The parity bit for the parity row is: 1

4. The bit that was flipped in figure 2 is (6,0):

11001101 00001101 1

10010010 00111000 0

00111001 00001110 1

10101100 10101110 1

01101101 00100011 0

10100101 10110110 1

For figure 3, the bit that was flipped is (14,1):

11110100 00101101 1

11001100 01110011 0

11101111 10110111 1

10011001 10111011 0

10111110 01010111 1

11110000 00000111 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: 0100101011000101

The answer was: 11111

The answer was: 1

The answer was: 6,0

The answer was: Yes