<p>Shor is probably referring to <a href="https://www.youtube.com/watch?v=VhyoZSB9g0w" rel="nofollow noreferrer">this</a> fantastic lecture by Emre Telatar that walks you through the steps in polar coding. Do watch it! In doing so, you shall see that the best mental model to have in mind while trying to wrap your head around the polar code is the erasure channel.</p>

CC BY-SA 3.0
2018-04-11T12:01:43.790Z
Yes, that is a very nice way of getting to an understanding of polar codes.
kodlu
CC BY-SA 3.0
2018-04-07T01:55:44.840Z
2018-04-07T01:55:44.840Z
WiFO215
<p>I remember that it's by recursion procedure, and the initial condition $N=1$, $h_{1}(y)=\dfrac{W(y|0)}{W(y|1)}$. Then base on the $W$ channel's transmite probability and received value.</p>

CC BY-SA 3.0
2018-03-07T02:54:30.193Z
2018-03-07T02:54:30.193Z
Chris LIU
<p>Polar decoding, according to <a href="http://arxiv.org/pdf/0807.3917.pdf" rel="nofollow noreferrer">Arikan's paper</a>, can be decoded using a successive cancellation (SC) decoder, which is based on calculating the likelihood ratio, as seen in the image below.</p>

<p><img src="https://i.sstatic.net/79Ppb.jpg" alt="Polar decoding equations"></p>

<p>How can I calculate equations 2 and 3 in the above image?
For example, assuming that $N=4$ and that we are using an AWGN channel with $\sigma=0.987$.</p>

CC BY-SA 3.0
2013-09-09T20:20:59.110Z
***Why the downvotes?*** Please explain. If we're going to new users here who ask questions here without giving any reasons for them, we're going to drive everybody away. Polar coding is one of the great recent advances in coding theory, and the paper is not all that easy to understand.
Peter Shor 
CC BY-SA 3.0
2013-09-09T20:30:12.603Z
I don't know why you were downvoted, but I can try to help you improve the question. People here like to see some indication of effort on the part of the poster trying to answer it themself ... I don't know whether this is the reason for the downvotes, but it would help if you told us what you tried already. It would also help to explain some of the terms: for example, SC, AWGN and sigma.
Peter Shor 
CC BY-SA 3.0
2013-09-10T12:27:16.453Z
There are a number of subsequent papers about polar coding, some of which do a better job of explaining it. There was a tutorial about polar coding at one of the ISITs (international symposia on information theory), and if they have the slides on-line, I think they would be helpful. I don't have time to look for references right now, though.
Peter Shor 
CC BY-SA 3.0
2013-09-10T12:29:40.503Z
For SC decoder:Successive cancellation decoder depends on the iterative calculation of likelihood ratio to recover original message                                                              AWGN : additive white gaussian noise channel i think the type of channel has something to do with calculation of LLR at decoder but i don't understand how.                                          sigma is the variance related to AWGN channel
Abdalkhalik
CC BY-SA 3.0
2013-09-10T18:34:54.310Z
**Downvoters:** I suspect the OP is trying to understand a particular step in this ground-breaking paper by asking how to do this calculation, which is important for the paper but I believe isn't explained very well ... I expect he is asking for specific numbers because he thinks it will be easier to understand by seeing how an example works rather than having an explanation of the general procedure. So he's essentially asking for an explanation of a particular step in this paper. This should be research level. I'd answer, but I've only looked at polar coding for the binary symmetric channel.
Peter Shor 
CC BY-SA 3.0
2013-09-20T17:02:04.183Z
What is each of the variables here? You have to explain this for people to have motivation.
Turbo
CC BY-SA 3.0
2013-09-21T00:04:27.483Z
If you found the answer, it would be polite to post an answer on what you found.
Turbo
CC BY-SA 3.0
2014-01-12T13:01:30.290Z
@PeterShor I just downvoted, but didn't cast a close vote. I agree with you that the topic is interesting and in-scope, however downvotes (at least for me) are not used to indicate relevance of topic (as close votes are) but also style and clarity. The OP seemed to have invested very little time into asking the question, I would prefer not to encourage such hasty write ups because they seem disrespectful to the community.
Artem Kaznatcheev
<it.information-theory><coding-theory>
Explanation of polar decoding?
Abdalkhalik
# Explanation of polar decoding?

(Asked by: username_0 on 2013-09-08)

Polar decoding, according to [Arikan's paper](http://arxiv.org/pdf/0807.3917.pdf), can be decoded using a successive cancellation (SC) decoder, which is based on calculating the likelihood ratio, as seen in the image below.

![Polar decoding equations](https://i.sstatic.net/79Ppb.jpg)

How can I calculate equations 2 and 3 in the above image?
For example, assuming that $N=4$ and that we are using an AWGN channel with $\sigma=0.987$.

**Tags:** it.information-theory, coding-theory
> **Comments:**
> **username_1**: ***Why the downvotes?*** Please explain. If we're going to new users here who ask questions here without giving any reasons for them, we're going to drive everybody away. Polar coding is one of the great recent advances in coding theory, and the paper is not all that easy to understand.  
> **username_1**: I don't know why you were downvoted, but I can try to help you improve the question. People here like to see some indication of effort on the part of the poster trying to answer it themself ... I don't know whether this is the reason for the downvotes, but it would help if you told us what you tried already. It would also help to explain some of the terms: for example, SC, AWGN and sigma.  
> **username_1**: There are a number of subsequent papers about polar coding, some of which do a better job of explaining it. There was a tutorial about polar coding at one of the ISITs (international symposia on information theory), and if they have the slides on-line, I think they would be helpful. I don't have time to look for references right now, though.  
> **username_0**: For SC decoder:Successive cancellation decoder depends on the iterative calculation of likelihood ratio to recover original message                                                              AWGN : additive white gaussian noise channel i think the type of channel has something to do with calculation of LLR at decoder but i don't understand how.                                          sigma is the variance related to AWGN channel  
> **username_1**: **Downvoters:** I suspect the OP is trying to understand a particular step in this ground-breaking paper by asking how to do this calculation, which is important for the paper but I believe isn't explained very well ... I expect he is asking for specific numbers because he thinks it will be easier to understand by seeing how an example works rather than having an explanation of the general procedure. So he's essentially asking for an explanation of a particular step in this paper. This should be research level. I'd answer, but I've only looked at polar coding for the binary symmetric channel.  
> **username_2**: What is each of the variables here? You have to explain this for people to have motivation.  
> **username_2**: If you found the answer, it would be polite to post an answer on what you found.  
> **username_3**: @PeterShor I just downvoted, but didn't cast a close vote. I agree with you that the topic is interesting and in-scope, however downvotes (at least for me) are not used to indicate relevance of topic (as close votes are) but also style and clarity. The OP seemed to have invested very little time into asking the question, I would prefer not to encourage such hasty write ups because they seem disrespectful to the community.  

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## 2 answers

### Answer by username_4 on 2018-04-07. Score: 2

Shor is probably referring to [this](https://www.youtube.com/watch?v=VhyoZSB9g0w) fantastic lecture by Emre Telatar that walks you through the steps in polar coding. Do watch it! In doing so, you shall see that the best mental model to have in mind while trying to wrap your head around the polar code is the erasure channel.

> **Comments:**
> **username_5**: Yes, that is a very nice way of getting to an understanding of polar codes.  

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### Answer by username_6 on 2018-03-07. Score: 0

I remember that it's by recursion procedure, and the initial condition $N=1$, $h\_{1}(y)=\dfrac{W(y|0)}{W(y|1)}$. Then base on the $W$ channel's transmite probability and received value.


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