Virtual Labs

Consider a code

\mathcal{C}

with generator matrix

G = \begin{bmatrix} 1 & 0 & 1 & 0 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 & 0 \end{bmatrix}

, Select the matrix which is

\textbf{not}

a parity check of the code.

\begin{bmatrix} 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1\end{bmatrix}

Explanation

\begin{bmatrix} 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 & 0 & 1\end{bmatrix}

Explanation

\begin{bmatrix} 0 & 1 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1\end{bmatrix}

Explanation

\begin{bmatrix} 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1\end{bmatrix}

Explanation

e: None Explanation

Explanation

For the message

\textbf{m} = \left(1,0,0,1\right)

find correct codeword if generator matrix is

G = \begin{bmatrix} 1 & 0 & 1 & 0 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}

\left(0,0,1,0,1,1\right)

Explanation

\left(1,0,1,0,1,1\right)

Explanation

\left(1,0,0,0,0,0\right)

Explanation

\left(0,0,0,0,0,0\right)

Explanation

Consider a code

\mathcal{C}

with parity-check matrix

H = \begin{bmatrix} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 \end{bmatrix}

. Find a invalid codeword of

\mathcal{C}

\left(1,0,1,1\right)

Explanation

\left(0,0,0,0\right)

Explanation

\left(1,1,1,0\right)

Explanation

\left(0,1,1,1\right)

Explanation

Consider a noiseless-communication system with code

\mathcal{C}

and corresponding parity-check matrix

H = \begin{bmatrix} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 \end{bmatrix}

and receiver received codeword

\left(1,1,1,0\right)

. Find a correct (generator matrix, transmitted message) pair.

G = \begin{bmatrix} 0 & 1 & 0 & 1 \\ 1 & 1 & 1 & 0 \end{bmatrix}

and message transmitted be

\left(1,0\right)

Explanation

G = \begin{bmatrix} 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 \end{bmatrix}

and message transmitted be

\left(0,1\right)

Explanation

G = \begin{bmatrix} 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 1 \end{bmatrix}

and message transmitted be

\left(1,1\right)

Explanation

G = \begin{bmatrix} 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 \end{bmatrix}

and message transmitted be

\left(1,1\right)

Explanation

Consider a code

\mathcal{C}

with generator matrix

G = \begin{bmatrix} 1 & a & 1 & 0 \\ 0 & 1 & 1 & 1 \end{bmatrix}

. Suppose symbol

a

can take either 0 or 1. Which of the following statements are true?

a: If the message is

\left(1,0\right)

, the corresponding codeword is

\left(1,1,1,0\right)

, given

a=0

. Explanation

Explanation

b: If the message is

\left(1,1\right)

, the corresponding codeword is

\left(1,1,0,1\right)

, given

a=1

. Explanation

Explanation

c: If the message is

\left(1,0\right)

, the corresponding codeword is

\left(1,0,1,0\right)

, given

a=0

. Explanation

Explanation

d: If the message is

\left(0,0\right)

, the corresponding codeword is

\left(1,0,1,0\right)

, given

a=1

. Explanation

Explanation

Review of Block Codes