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.


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

dnd 5e – 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?


  • 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.

Youtube Channel Name suggestions welcome …!

Hello everybody,

In search of a name for a You Tube channel, the channel will soon be launched and the content will be divided into different categories, ranging from business tips to investments to travel and food reviews. It's like a general man’s channel. The boy's name starts with M..

Let's say his name is Mike and he's looking for suggestions for the channel name with his name. To like Mike's message or something special.

I hope I get some interesting suggestions.


How to get Keywords under Organic Channel?

Hello all
Greetings of the day!
Hope you all are doing well and safe. I'm working in a digital marketing agency Dubai

It is always showing "not provided" when I am searching for the actual keywords what the users are searching for my website under the channel group "Organic". Hoe can I resolve this issue. Thanks in advance for your replies.

magento2 – Amazon Sales Channel extension for Magento 2.3.3

Does the Amazon Sales Channel extension version 4.1 work on Magento 2.3.3? It doesn’t seem to. I installed the extension per the documenation, added the Production API Key from my Magento Marketplace account to the System and when I go to Marketing -> Channels -> Amazon I get the error Unexpected network error, please try again later.

Further inspection in the console shows the error: Error: GraphQL error: Internal server error

And when I click on Add Amazon Store it pops a window saying: Connection error Unable to create a new store. Please try again later.

I’m on Magento 2.3.3 with PHP 7.1.33

boot – error channel 1 could not be deactivated during the installation of Ubuntu 20.04

I am trying to install Ubuntu 20.04LTS on my Dell Inspiron 15 Gaming 5577 laptop. I flashed it with Rufus on my USB stick. First I got to the Ubuntu loading screen and my PC was shut down.
After that I switched off the quick start and now it's over, but it freezes and a black screen appears with this message and then I have to reset my PC.
Enter the image description here

nouveau 0000: 01: 00.0: DRM: Channel 1 [DRM] could not become inactive
My laptop specifications are as follows:
Bios 1.1.3, Nvidia Gtx 1050 4 GB, Intel Corei7-7700HQ and 16 GB RAM