[Discuss-gnuradio] SOCIS project update 6

[Johannes Demel]

Hey GNU Radio'ers!

It is time for another project update.
I started the week with a quick test if I could improve successive
cancellation list decoding. Though, I wanted to focus on channel
construction this week. So I did.
For polar codes one might consider different binary discrete memoryless
channels (BDMC). The easiest ones to calculate and find a suitable set
of frozen bit positions are Binary Erasure Channel (BEC) channels. The
algorithm just runs fine even for larger block sizes. So one could use
it on the fly.
But what has to be done in order to do channel construction?
First, calculate the capacities or Bhattacharyya
parameters(z-parameters), or if you want BERs, for every channel within
a polar code vector channel. Then choose the K channels with highest
capacity/lowest z-parameters and use them for your info bits.
The tricky part is to calculate those values. As said before, this is
easy for BEC. Also, those values represent an upper bound on
z-parameters. Exact calculations for other channels, like Binary
Symmetric Channels (BSC) or Binary AWGN (BAWGN) channels, are intracable
because the complexity for such an algorithm grows too large.
The algorithm mostly cited in papers was published by Tal and Vardy [3].
But other papers [4] claim that it is sufficient to use the simple and
fast algorithm for BEC. In fact the Tal-Vardy algorithm uses the BEC
algorithm too. But only to make sure z-parameters are always below or
equal this upper bound.
Of course the algorithm for BEC is implemented. Also, Tal-Vardy's
algorithm is implemented now. Though the results are not yet consistent.
It seems like this needs some more attention.

Next week, I will finish channel construction. I intend to create a
block which serves as a provider for polar encoder/decoder
parametrization. Afterwards I'll return to encoder/decoder optimizations.

More info and current project progress can be found in [1] and [2].

Cheers
Johannes

[1] https://github.com/jdemel/gnuradio
[2] https://github.com/jdemel/socis-proposal
[3] http://arxiv.org/pdf/1105.6164.pdf
[4] http://arxiv.org/abs/1501.02473