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.