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Aim

Pretest

Theory

Procedure

Simulation

Posttest

References

Contributors

Feedback

LDPC Codes: Introduction

Choose difficulty:

Beginner

Intermediate

Advanced

1. Consider the parity-check matrix

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

over

GF(2)

. What is the rank of this matrix?

a: 1 Explanation

Explanation

b: 2 Explanation

Explanation

c: 3 Explanation

Explanation

d: 4 Explanation

Explanation

2. For the parity-check matrix

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

, which equation represents the first parity check?

a:

c_1 + c_3 + c_4 = 0

Explanation

Explanation

b:

c_2 + c_4 + c_5 = 0

Explanation

Explanation

c:

c_1 + c_2 + c_4 = 0

Explanation

Explanation

d:

c_1 + c_3 + c_5 = 0

Explanation

Explanation

3. Given

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

, which of the following is a valid codeword?

a:

[1, 1, 1, 1]

Explanation

Explanation

b:

[1, 0, 1, 1]

Explanation

Explanation

c:

[1, 1, 1, 0]

Explanation

Explanation

d:

[0, 1, 0, 1]

Explanation

Explanation

4. A graph

G(V, E)

is called bipartite if

V

can be partitioned into

V_1

and

V_2

such that no edge connects two vertices of the same partition. What is the maximum number of edges a bipartite graph can have?

a:

|V_1| + |V_2| - 1

Explanation

Explanation

b:

|V_1| \times |V_2|

Explanation

Explanation

c:

2(|V_1| + |V_2|)

Explanation

Explanation

d:

\frac{|V_1| \times |V_2|}{2}

Explanation

Explanation

5. If a parity-check matrix has

n

columns and its rows are all linearly independent, what is the rank of the matrix?

a: The number of columns (

n

) Explanation

Explanation

b: The number of rows (

n-k

) Explanation

Explanation

c: The code rate (

R

) Explanation

Explanation

d: Always 1 Explanation

Explanation

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