Virtual Labs

Message Passing Decoding of LDPC Codes on Erasure Channel

1. Consider the code

\mathcal{C} = \{\boldsymbol{x_1}=(0,0,0,0,0), \boldsymbol{x_2}=(1,0,1,0,1), \boldsymbol{x_3}=(0,1,0,1,1), \boldsymbol{x_4}=(1,1,1,1,0) \}

. Suppose a codeword from

\mathcal{C}

is transmitted over a

BEC(\epsilon)

. Choose the option corresponding to the output of ML decoder if the received vector is

\boldsymbol{y}=(1,?,1,?,0)

(0,0,0,0,0)

Explanation

(1,1,1,1,0)

Explanation

(0,1,0,1,1)

Explanation

(1,0,1,0,1)

Explanation

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

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

Explanation

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

Explanation

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

Explanation

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

Explanation

3. Find the vector

(x, y) \in \mathbb{F}_3^2

which satisfies the following constraints:

\begin{aligned} x + 2y &= 2 \\ 2x - y &= 1 \end{aligned}

(\frac{4}{5}, \frac{3}{5})

Explanation

(1, 2)

Explanation

(2, 0)

Explanation

(1, 0)

Explanation

4. Write the parity check equations corresponding to the following Tanner graph

x_0 + x_2 + x_3 + x_5 = 1, x_1 = 1, x_0 + x_2 + x_3 + x_5 = 0

Explanation

x_0 + x_2 + x_4 = 0, x_1 + x_3 + x_5 = 0, x_2 + x_4 + x_6 = 0

Explanation

x_0 + x_2 + x_3 + x_5 = 1, x_1 = 1, x_0 + x_2 + x_4 + x_5 = 0

Explanation

x_2 + x_3 + x_5 = 0, x_0 + x_4 + x_6 = 0, x_2 + x_5 + x_6 = 0

Explanation