Virtual Labs

Message Passing Decoding of LDPC Codes on Other Channels

What is the primary goal of the Bit-wise MAP decoding algorithm?

a: To find the most likely transmitted codeword from the entire codebook. Explanation

Explanation

b: To determine the most probable value for each individual bit of the codeword, given the received vector. Explanation

Explanation

c: To calculate the noise variance

\sigma^2

of the AWGN channel. Explanation

Explanation

d: To verify if the Tanner graph of the code is cycle-free. Explanation

Explanation

If the final Log-Likelihood Ratio

L(x_i)

for a bit is calculated to be

-3.5

, what is the bit-wise MAP estimate

\hat{x}_i

a: 0 Explanation

Explanation

b: 1 Explanation

Explanation

c: The value cannot be determined. Explanation

Explanation

d: An erasure is declared. Explanation

Explanation

In the provided example, the received value for the first bit is

y_0 = -0.5

and the noise variance is

\sigma^2 = 0.5

. What is the initial channel LLR,

L_{ch}(x_0)

a: -1.0 Explanation

Explanation

b: -0.5 Explanation

Explanation

c: -2.0 Explanation

Explanation

d: +2.0 Explanation

Explanation

What is the formula for the message sent from a variable node

v_i

to a check node

c_j

during iteration

k

L_{i \to j}^{(k)} = L_{ch}(x_i)

Explanation

L_{i \to j}^{(k)} = \sum_{j' \in N(v_i) \setminus \{j\}} L_{j' \to i}^{(k-1)}

Explanation

L_{i \to j}^{(k)} = L_{ch}(x_i) + \sum_{j' \in N(v_i) \setminus \{j\}} L_{j' \to i}^{(k-1)}

Explanation

L_{i \to j}^{(k)} = L_{ch}(x_i) + \sum_{j \in N(v_i)} L_{j \to i}^{(k)}

Explanation

A check node

c_j

receives three incoming messages with values:

-2.5

+3.0

, and

+1.5

. According to the Min-Sum rule, what message does it send to the variable node that originally sent the message

-2.5

a: +1.5 Explanation

Explanation

b: -1.5 Explanation

Explanation

c: +3.0 Explanation

Explanation

d: -2.5 Explanation

Explanation

Which of the following is a valid termination condition for the Min-Sum algorithm?

a: All LLR values become positive. Explanation

Explanation

b: The number of iterations exceeds the number of variable nodes. Explanation

Explanation

c: The hard decision vector

\hat{\bm{x}}^{(k)}

satisfies all parity checks. Explanation

Explanation

d: The messages sent from variable nodes to check nodes become zero. Explanation

Explanation

Based on the Check Node update rule, if a check node

c_j

is connected to only two variable nodes

v_i

and

v_{i'}

, what is the message

L_{j \to i}^{(k)}

L_{j \to i}^{(k)} = L_{i' \to j}^{(k)}

Explanation

L_{j \to i}^{(k)} = -L_{i' \to j}^{(k)}

Explanation

L_{j \to i}^{(k)} = \min(|L_{i' \to j}^{(k)}|, 0)

Explanation

L_{j \to i}^{(k)} = 0

Explanation

What is the initial value of all messages from check nodes to variable nodes,

L_{j \to i}^{(0)}

, before the first iteration begins?

a: They are initialized to the channel LLRs. Explanation

Explanation

b: They are initialized to 1. Explanation

Explanation

c: They are initialized to infinity. Explanation

Explanation

d: They are initialized to 0. Explanation

Explanation