Polar Codes in Python

A library written in Python3 for Polar Codes, a capacity-achieving channel coding technique used in 5G. The library includes functions for construction, encoding, decoding, and simulation of polar codes. In addition, it supports puncturing and shortening.

It provides:

• a systematic and non-systemic encoder.
• non-recursive implementations of the successive cancellation decoder (SCD).
• mothercode construction of polar codes using Bhattacharyya Bounds or Gaussian Approximation
• support for puncturing and shortening.
• Bit-Reversal Shortening (BRS), Wang-Liu Shortening (WLS), and Bioglio-Gabry-Land (BGL) shortening constructions.
• an AWGN channel with BPSK modulation.
• an easy-to-use Graphical User Interface (GUI)

Documentation:

• Main reference (pdf)
• Quick reference (website)
• Introduction to polar codes, shortening, and the library: http://www.youtube.com/watch?v=v47rn77RAxM

Getting Started

1. Install the package with pip install py-polar-codes from https://pypi.org/project/py-polar-codes/.
2. Install matplotlib from https://matplotlib.org/users/installing.html.
3. Install numpy from https://docs.scipy.org/doc/numpy/user/install.html.
4. Run test.py using a Python3 compiler. If the program runs successfully, the library is ready to use. Make sure the compiler has writing access to directory "root/data", where simulation data will be saved by default.
5. Call GUI() to start the GUI.

Examples

Mothercode Encoding & Decoding

An example of encoding and decoding over an AWGN channel for a (256,100) non-systematic mothercode, using Bhattacharyya Bounds for construction and SCD for decoding. For systematic encoding and decoding, replace Encode(myPC) with Encode(myPC, 'systematic_encode') and Decode(myPC) with Decode(myPC, 'systematic_scd').

   import numpy as np
   from polarcodes import *

    # initialise polar code
    myPC = PolarCode(256, 100)
    myPC.construction_type = 'bb'
    
    # mothercode construction
    design_SNR  = 5.0
    Construct(myPC, design_SNR)
    print(myPC, "\n\n")
    
    # set message
    my_message = np.random.randint(2, size=myPC.K)
    myPC.set_message(my_message)
    print("The message is:", my_message)
    
    # encode message
    Encode(myPC)
    print("The coded message is:", myPC.get_codeword())
    
    # transmit the codeword
    AWGN(myPC, design_SNR)
    print("The log-likelihoods are:", myPC.likelihoods)
    
    # decode the received codeword
    Decode(myPC)
    print("The decoded message is:", myPC.message_received)

Shortened Code Construction

An example of constructing a shortened polar code with Bit-Reversal Shortening (BRS) algorithm. The shortening parameters are set by the tuple shorten_params, the third argument of PolarCode, and is defined by:

• Puncturing type: shorten or punct.
• Puncturing algorithm: brs, wls, or bgl.
• Puncturing set (for manual puncturing): ndarray<int>
• Overcapable set (for manual puncturing): ndarray<int>
• Update reliabilities after puncturing (or use mothercode reliabilities): True or False.

   import numpy as np
   from polarcodes import *

    # initialise shortened polar code
    shorten_params = ('shorten', 'brs', None, None, False)
    myPC = PolarCode(200, 100, shorten_params)
    
    # construction
    design_SNR  = 5.0
    Shorten(myPC, design_SNR)
    print(myPC, "\n\n")

Simulation & Plotting

A script to simulate a defined polar code, save the data to directory "/data", and then display the result in a matplotlib figure.

    # simulate polar code 
    myPC.simulate(save_to='data/pc_sim', Eb_No_vec=np.arange(1,5), manual_const_flag=True)
    
    # plot the frame error rate
    myPC.plot(['pc_sim'], 'data/')

The simulation will save your PolarCode object in a JSON file, for example:

{
    "N": 64,
    "n": 6,
    "K": 32,
    "frozen": [
        22, 38, 49, 26, 42, 3, 28, 50, 5,44,9, 52, 6, 17, 10, 33, 56, 18, 12, 34, 20, 36, 1, 24, 40, 48, 2, 4, 8, 16, 32, 0
    ],
    "construction_type": "bb",
    "punct_flag": false,
    "punct_type": "",
    "punct_set": [],
    "source_set": [],
    "punct_algorithm": "",
    "update_frozen_flag": [],
    "BER": [
        0.09709375, 0.03740625, 0.00815625, 0.0010184612211221122
    ],
    "FER": [
        0.313, 0.126, 0.03,0.004125412541254125
    ],
    "SNR": [
        1, 2, 3, 4
    ]
}

Graphical User Interface

An example of using the GUI to simulate and plot a specified polar code. Note: if "manual construction" is ticked, the user is required to input the frozen bits and the shortened bits.

This is a final year project created by Brendon McBain under the supervision of Dr Harish Vangala at Monash University.