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Aim

Pretest

Theory

Procedure

Simulation

Posttest

References

Contributors

Feedback

Maximum Likelihood Decoding of Linear Codes on Binary-Input Memoryless Channels

Choose difficulty:

Beginner

Intermediate

Advanced

1. Consider a Gaussian distribution given by its pdf

f(x) = \frac{1}{5\sqrt{2\pi}}e^{-\frac{(x-\pi)^2}{50}}

. Choose the correct options for the mean and variance, respectively, for the given distribution.

5, \pi

Explanation

\pi, 5

Explanation

25, \pi

Explanation

\pi, 25

Explanation

2. Suppose

A = \{1, \pi, 3, 2.8, -5, 25\}

. Find

\hat{x} = arg \max_{x \in A} x^2

\pi

Explanation

25

Explanation

2.8

Explanation

-5

Explanation

3. Choose the correct option for given two statements.

\\ \text{1. BEC can flip bit value. }\\ \text{2. BSC can erase bit value.}

a: Both

1

and

2

are wrong. Explanation

Explanation

1

is correct,

2

is wrong. Explanation

Explanation

1

is wrong,

2

is correct. Explanation

Explanation

d: Both

1

and

2

are correct. Explanation

Explanation

4. Let

\mathcal{C} =

\{(0,0,0,\cdots,0),

(1,1,1,\cdots,1)\}

be a

n

-length code. Suppose a codeword from

\mathcal{C}

is transmitted over a

BEC(\epsilon)

. Find the maximum number of erasures that allows unambiguous recovery of the transmitted codeword.

\frac{n}{2}

Explanation

\frac{n-1}{2}

Explanation

n-1

Explanation

1

Explanation

5. Suppose

\textbf{x}

= (1,0,1,1)

is being transmitted over Binary Symmetric Channel. Choose the valid received vector.

(0,1,1,1)

Explanation

(0,1,1)

Explanation

(1,?,1,1)

Explanation

(1,0,?,1)

Explanation

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