Channel coding and Error probability. Where are these probabilities from?

From where are the following probabilities?

We consider BSCε with ε = 0,1 and block code C = {c1, c2} with the code words c1 = 010 and c2 = 101. On the received word y we use the decoder D = {D1,D2} which decodes the word to the code word which has the lowest hamming distance to y. Determine D1 and D2 and the global error probability ERROR(D) if the code words have the same probability. Hint: To an output y there exists only one x which gets to a failing decoding. (Y = 100 will only gets wrong decoded if we sent message is x = c1 = 010.) So the term (1− p(D(y)|y)) is equal to Pr[X = x|Y = y] for a suitable x.

Nun

$ $ \begin{aligned} &\text { Hamming-Distance: }\ &\begin{array}{c|cc} \text { Code } & 010 & 101 \ \hline \hline 000 & 1 & 2 \ \hline 001 & 2 & 1 \ \hline 010 & 0 & 3 \ \hline 011 & 1 & 2 \ \hline 100 & 2 & 1 \ \hline 101 & 3 & 0 \ \hline 110 & 1 & 2 \ \hline 111 & 2 & 1 \ \hline \end{array} \end{aligned}$ $ $ $ \left.D_{1}=\{000,010,011,110\} \text { (Decides for } 010\right)$ $ \left.D_{2}=\{001,100,101,111\} \text { (Decides for } 101\right)$ $ $ $ \begin{aligned} E R R O R(D) &=\sum_{y \in \Sigma_{A}^{3}} p(y)(1-p(D(y) | y)) \ &=\overbrace{2 \cdot p(y)(1-p(D(y) | y))}+\quad \overbrace{6 \cdot p(y)(1-p(D(y) | y))}^{ } \ &=2 \cdot\left(\frac{729}{2000}+\frac{1}{2000}\right)\left(\frac{7}{250}\right)+6 \cdot\left(\frac{81}{2000}+\frac{9}{2000}\right)\left(\frac{757}{1000}\right) \end{aligned}$ $ How do I get to the probabilities $ $ \frac{7}{250}$ $ and $ $ \frac{757}{1000}$ $ ??

I don’t get this calculation. It should be right. But I don’t get how to get to these probabilities.

Could someone explain me this?

What is exactly erasure channel?

Can anyone explain to me what is exactly erasure channel which occur beside single-bit error and burst error? I read on the internet but I couldn’t really grasp and imagine what exactly erasure channel is. Links for reference also will be welcomed about erasure channel. Thank you.

If I cast Thunderous Smite and Booming Blade, hit, and use Destructive Wrath to maximize damage, how many uses of Channel Divinity are expended?

How many uses of channel divinity should be expended in the following example?

Example:

  • A character is using that a weapon that deals 2d6 thunder damage on a hit.
  • They cast Thunderous Smite, using a bonus action.
  • Then cast Booming Blade (at 5th level), making a melee attack as an action.
  • On a hit, the weapon does an additional 1d8 + 2d6 + 2d6 thunder damage.

Thunderous Smite:

The first time you hit with a melee weapon attack during this spell’s duration, your weapon rings with thunder that is audible within 300 feet of you, and the attack deals an extra 2d6 thunder damage to the target.

Booming Blade:

At 5th level, the melee attack deals an extra 1d8 thunder damage to the target, and the damage the target takes for moving increases to 2d8.

Destructive Wrath:

When you roll lightning or thunder damage, you can use your Channel Divinity to deal maximum damage, instead of rolling.

I’m interpreting this as three separate rolls for thunder damage, each requiring a use of Channel Divinity to maximize. Instead of one use of Channel Divinity to maximize all of them at once.

One of the main reasons I’m thinking this, is because another use of Channel Divinity needs to be expended to maximize the secondary damage from Booming Blade, as it’s a completely separate roll.

Microphone channel not detected in Unity

This is very specific to Unity.

A few testers are reporting that their microphone output isn’t being detected. The code below works for the vast majority of users, but certain microphones seem to be outputting on the wrong channel (R maybe)?

 AudioClip current_microphone_recording_clip = Microphone.Start(microphone_name, true, 30, 16000); 

How can I capture and analyze output from several channels? I don’t see any channels parameter for Microphone.Start

Cleric Channel Energy heals and damages at the same time?

Can a Cleric use Channel Positive Energy to damage and heal at the same time?

For example: An undead and a living human are 10 feet from the cleric. The cleric Channels Positive Energy. Does he damage the undead and heal the human?

If he can only heal or cause damage, and not both at the same time, why not? There is not much sense behind this. If it is a burst of Positive Energy shouldn’t it affect all in the area in some way? How does Positive Energy stops healing living creatures or stops causing damage to undead?

Capacity of a discrete memoryless channel

For an integer $ I$ , the input-output relationship of a discrete memoryless channel is given by:

$ Y = X + Z$ (mod I, i.e. sum indicates a modular addition)

where $ I ≥ 2$ , and

• X is an integer chosen from the alphabet Ax = {1,…,2I},

• Z is noise which is a uniform Bernoulli random variable. This means that Az = {0,1}, and

Pr{Z = 0} = Pr{Z = 1} = 0.5.

How can we calculate the capacity of this channel?

What are the main differences between a covert timing channel and a covert storage channel?

I am trying to find the differences between a covert timing channel and a covert storage channel in terms of detectability, performance, features, and any other advantages and disadvantages.

Is there any resource that directly compares the advantages and disadvantages of the two attacks?