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I have tried searching for explanations for breaking down lifting schemes. The context of this question lies in complex multiplication. The authors have decomposed complex multiplications through a series of lifting steps.

After tirelessly searching for an intuitive tutorial on lifting schemes, I've realized that perhaps I don't have the mathematical background to tackle such a task.

My question is: how did we decompose a complex multiplication into the above lifting steps? Any tutorials/hints/links are appreciated!

UPDATE: Context: The above lifting scheme complex multiplication was developed in an IEEE paper by Soontorn Oraintara, Ying-Jui Chen, Truong Q. Nguyen located at this link: http://www-ee.uta.edu/msp/pub/Journaintfft.pdf

In page 4 of their paper, they explain how a complex multiplication can be broken down into lifting steps. I'm not making that connection. Specifically, I don't understand how to interpret the diagram. I have searched for numerous examples on how lifting schemes work with no avail. I've ordered a few textbooks on the subject, but I was wondering if anyone could point me to the correct direction on these problems.

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It's explained in this paper: s3.amazonaws.com/files.posterous.com/docjava/…. How did you end up with this image without the paper it belongs to? –  joriki Jul 10 '11 at 23:51
I was reading the paper that you linked to... but could not find any elaboration on how the actual lifting scheme is computed. (ie: with an example) –  Carlo del Mundo Jul 11 '11 at 3:36
I find it somewhat disrespectful that you read a paper that has a lot of background on this, then copy an image from it and throw it at us without any context or explanation whatsoever for the symbols in it -- why do you let us guess about all this when you already know the background and could post a link to it? –  joriki Jul 11 '11 at 4:00
Under no circumstance was I trying to be disrespectful. The paper contains dense information on the subject. I came to ask a question here because I can't determine whether my question is due to lack of content knowledge or is due to some arcane topic. –  Carlo del Mundo Jul 11 '11 at 15:48
Which part of what I wrote did you perceive as derisive? That wasn't my intention and I apologize if that was your impression. In my first comment, I assumed that you didn't know the paper since you didn't tell us about it, and merely wondered how you came across the image without the paper; in my second comment, my intention was not derision but criticism of your attitude towards this forum. I do think that this is a big problem; you're by far not the only one to post questions taken out of context, and we all have a responsibility to keep that from happening since it wastes everyone's time. –  joriki Jul 11 '11 at 16:04
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