The algorithms are either direct implementations of the standard polar coding literature or they are Matlab implementions of the pseudo-code presented in the papers below.
Recent
publications
Matlab codes- H. Vangala, E. Viterbo, and Yi Hong, "Efficient systematic polar encoding", IEEE Communication Letters, 2015.
- H. Vangala, E. Viterbo, and Yi Hong, "A Comparative Study of Polar Code Constructions for the AWGN Channel", Jan. 2015.
- H. Vangala, E. Viterbo, and Yi Hong,
"A new multiple
folded successive cancellation decoder for polar codes", Information
Theory Workshop, ITW 2014,
- H. Vangala, E.
Viterbo, and Yi Hong, "Permuted
successive cancellation decoder for polar codes", International
Symposium on Information Theory and its Applications, ISITA 2014,
- H. Vangala, E.
Viterbo, and Yi Hong, "Improved
Multiple Folded Successive Cancellation Decoder for Polar Codes", General
Assembly and Scientific Symposium (URSI GASS),
We have created a MATLAB module that has all the components of polar
codes. More specifically, we have implemented following components in
full detail.
- Polar code design: Based on the recursive estimation of Bhattacharyya parameters of bit-channels [2]
- Encoding: Non-systematic polar encoder
- Decoding: Successive Cancellation Decoding
- Systematic encoding: All 3 algorithms from [1]
- Decoding under systematic encoding: Successive Cancellation Decoding
The system model and various functions can be visualized using the below block digram.
Installation
The code is a standalone directory. It can simply be copied/sourced directly into the current working directory of MATLAB.Alternatively you may add the full path of the extracted directory to your MATLAB path. This is more flexible that
you may call the polar coding routines from any working directory.
No other installation is required. One can instantly start working with polar coding modules.
Working Examples
INITIALIZATION:>> N=128; K=64; Ec=1; N0=2; %0dB SNR
>> initPC(N,K,Ec,N0);
All polar coding parameters/resources initialized. (in a global structure - "PCparams")
N: 128
K: 64
n: 7
FZlookup: [128x1 double]
Ec: 1
N0: 2
LLR: [1x255 double]
BITS: [2x127 double]
designSNRdB: 0
STANDARD POLAR CODING:
>> u= (rand(K,1)>0.5); %message
>> x= pencode(u); % POLAR ENCODING
>> y= (2*x-1)*sqrt(Ec) + sqrt(N0/2)*randn(N,1); %AWGN
>> u_decoded= pdecode(y); %SUCCESSIVE CANCELLATION DECODING
>> logical(sum(u==u_decoded)) %Check if properly decoded
ans =
1
SYSTEMATIC POLAR CODING:
>> x_systematic = systematic_pencode(u);
%optional, extra argument is the encoder-name: 'A'(default) or 'B' or 'C'
>> y= (2*x-1)*sqrt(Ec) + sqrt(N0/2)*randn(N,1); %AWGN
>> u_decoded= systematic_pdecode(y);
>> logical(sum(u==u_decoded))
ans =
1
PLOTTING THE PERFORMANCE CURVES:
>> N=128; K=64; EbN0range=0:0.4:2; designSNRdB=0;
>> plotPC(N,K,EbN0range,designSNRdB,0); %last argument says no VERBOSE-output
Completed SNR points (out of 6):
0.00 dB (time taken:27.69 sec)
0.40 dB (time taken:27.18 sec)
0.80 dB (time taken:27.18 sec)
1.20 dB (time taken:27.16 sec)
1.60 dB (time taken:27.10 sec)
2.00 dB (time taken:40.55 sec)
Eb/N0 range (dB) : 0 0.4000 0.8000 1.2000 1.6000 2.0000
Frame Error Rates: 0.7080 0.5930 0.4790 0.3730 0.2400 0.1342
Bit Error Rates : 0.2311 0.1776 0.1393 0.1012 0.0646 0.0317
>> plotPC_systematic(N,K,EbN0range,designSNRdB,0); %last argument says no VERBOSE-output
Completed SNR points (out of 6):
0.00 dB (time taken:31.66 sec)
0.40 dB (time taken:31.68 sec)
0.80 dB (time taken:31.84 sec)
1.20 dB (time taken:31.71 sec)
1.60 dB (time taken:31.94 sec)
2.00 dB (time taken:45.58 sec)
Eb/N0 range (dB) : 0 0.4000 0.8000 1.2000 1.6000 2.0000
Frame Error Rates: 0.7400 0.6050 0.4620 0.3140 0.2430 0.1395
Bit Error Rates : 0.1223 0.0906 0.0649 0.0386 0.0276 0.0142