How to implement polar codes (both encoding and decoding) in matlab?

PS: For a complete MATLAB package that can help you to immediately start working with polar codes, visit our recent site: www.polarcodes.com

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There are actually three components that you need to implement polar codes.

1. Construction Algorithm

2. Encoder Algorithm

3. Decoder Algorithm

Check this paper for a full implementation of the decoder & construction algorithms:

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6979881

OR

http://www.tinyurl.com/permutedpolar

Just set no-permutation or permutation specification vector $\underline{pi}$ = [n-1,n-2,...,0]

And the remaining encoder is an interesting puzzle left to you.

Hints:

1. The basic loops for encoder are same as that of a construction algorithm. Except that you need to first prepare an N-bit vector "d" which embeds K-bit message vector "u" in it, using the frozenbit locations.

2. Use "d" as input to the same three-loop algorithm

3. Replace (z^2-2z, z^2) operations with (x1+x2, x2) where '+' is bit-XOR. And the result is the encoded vector "x" = F^n "d"

PS: I have recently released a full MATLAB code-base using a logic much more efficient and improved upon the above paper. It is openly available here: http://www.ecse.monash.edu.au/staff/eviterbo/polarcodes.html

Simply put, the zip file provided there contains all basic components required for polar coding such as: 1. Construction 2. Encoding 3. Successive cancellation decoding

In fact, as a bonus, it even includes advanced (most efficient known) modules required for "systematic polar codes" as described in: http://dx.doi.org/10.1109/LCOMM.2015.2497220