Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An elementary description of polarization process   We analyze successive cancellation (SC) decoder by using two random
functions. The first function is related to the likelihoods of 0 and 1 in each
code position, while the second gives the difference between their posterior
probabilities. We then study the second power moments of both functions. We
show that these moments are being squared in channel transformations, while
their product tends to 0 for growing lengths $n$. This gives an elementary
proof of polarization properties of SC decoding. We also derive a simple
ordering of decoding channels with construction complexity of order $n\log n$.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th