Explanation of polar decoding?

Polar decoding, according to Arikan's paper, can be decoded using a successive cancellation (SC) decoder, which is based on calculating the likelihood ratio, as seen in the image below. 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 $\sigma=0.987$.

• 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. Sep 9 '13 at 20:20
• 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. Sep 9 '13 at 20:30
• 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. Sep 10 '13 at 12:27
• 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. Sep 10 '13 at 18:34
• If you found the answer, it would be polite to post an answer on what you found. Sep 21 '13 at 0:04

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.