C and MATLAB implementation for Polar encoding and decoding
This repository provides C and MATLAB implementations for polar codes.
For the seminal work on polar codes, please refer to: Erdal Arikan, "Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels", http://arxiv.org/abs/0807.3917
Encoding for polar codes
Decoding for polar codes including
Code construction:
AWGN simulations
The figure above shows the performance comparison between PolarC and Tal Fig. 1. A close comparison reveals that the performance for CRC aided polar code is about 0.1 dB worse. Note that the two key differences are (i) code construction method (ii) LLR based decoder with hardware-friendly (see Stimming) LLR updates for large values of LLRs.
** Update Nov, 2016 **
The figure above shows the results for modulation specific polar codes using the Gaussian approximation code construction for block length 1024 across a variety of rates and constellations. The results are close to the results given in Mathis.
The figure above shows the results for for modulation specific polar codes using the Monte Carlo code construction for block length 1024 and info length 512 codes. The results use link level simulations for AWGN channel using the SCD algorithm. The results for 4-ASK + PBP (Gray Labeling) are close to the results in Mahdavifar though there are some differences in the approach itself.
Runtime is mainly dominated by the decoder. The run time comparison for rate 1/2 code is as follows (run on a single macbook pro 2015):
Parameters | PolarC | PolarM | Speedup C/M |
---|---|---|---|
N = 2048, L = 1 | 250 | 51 | 5x |
N = 2048, L = 4 | 67 | 3.2 | 20x |
N = 2048, L = 32 | 10.1 | 0.65 | 15x |
N = 512, L = 1 | 890 | 204 | 4.5x |
N = 512, L = 4 | 287 | 14 | 20x |
N = 512, L = 32 | 44 | 2.8 | 16x |
The key code is in class PolarCode (C and MATLAB). The interface to this class is as follows:
constructor
encode (MATLAB code modified from Pfister)
decode_SC_P1 (only for MATLAB - code modified from Pfister)
decode_SCL_P1
decode_SCL_LLR
get_bler_quick (helper function)
Note that for speed up of simulation, get_bler_quick assumes that if a given run (as in info bit and noise realizations) is decoded for a lower EbNo value, then it will be decoded for a higher EbNo value.
The PolarC code will not compile with libstdc++. The code only works with libc++.
The code is provided as is without any warranty (implicit or explicit) and without guarantee of correctness.