Virtual Labs

1. Let

\mathcal{C}

be a regular LDPC code with a

5

-by-

6

parity-check matrix

H

of rank

3

. Select the correct pair for the

\textbf{ rate }

and

\textbf{ design rate }

of the code.

\textbf{ rate } = \frac{1}{2}

and

\textbf{ design rate } = \frac{1}{2}

Explanation

\textbf{ rate } = \frac{1}{6}

and

\textbf{ design rate } = \frac{1}{6}

Explanation

\textbf{ rate } = \frac{1}{6}

and

\textbf{ design rate } = \frac{1}{2}

Explanation

\textbf{ rate } = \frac{1}{2}

and

\textbf{ design rate } = \frac{1}{6}

Explanation

2. Select the correct parity-check matrix

H

for a

\textit{ regular }

LDPC code with block length

n = 6

and check nodes

n-k = 3

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

Explanation

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

Explanation

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

Explanation

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

Explanation

3. Which of the following is a characteristic property of a bipartite graph?

a: It contains at least one odd cycle. Explanation

Explanation

b: All vertices can be divided into two sets such that no two vertices within the same set are adjacent. Explanation

Explanation

c: All edges of the graph connect vertices within the same set. Explanation

Explanation

d: It contains an even number of vertices. Explanation

Explanation

4. Which of the following LDPC codes is expected to perform better in practice, particularly in terms of error correction capability, given sufficient large block length?

a: A regular LDPC code with large block lengths. Explanation

Explanation

b: An irregular LDPC code with large block lengths. Explanation

Explanation

c: A regular LDPC code with short block lengths. Explanation

Explanation

d: An irregular LDPC code with short block lengths. Explanation

Explanation

5. Choose the correct parity-check matrix that corresponds to the given Tanner graph:

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

Explanation

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

Explanation

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

Explanation

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

Explanation

LDPC Codes: Introduction