Cyclic Redundancy Check (CRC)
=============================

A cyclic redundancy check adds parity bits to detect transmission errors.

.. currentmodule:: sionna.phy.fec.crc
.. autosummary::
   :toctree: .

   CRCEncoder
   CRCDecoder



The following code snippets show how to add CRC parity bits to a bit sequence
and how to verify that the check is valid.

First, we need to create instances of :class:`~sionna.phy.fec.crc.CRCEncoder` and :class:`~sionna.phy.fec.crc.CRCDecoder`:

.. code-block:: Python

  encoder = CRCEncoder(crc_degree="CRC24A") # the crc_degree denotes the number of added parity bits and is taken from the 3GPP 5G NR standard.

  decoder = CRCDecoder(crc_encoder=encoder) # the decoder must be associated to a specific encoder


We can now run the CRC encoder and test if the CRC holds:

.. code-block:: Python

   # u contains the information bits to be encoded and has shape [...,k].
   # c contains u and the CRC parity bits. It has shape [...,k+k_crc].
   c = encoder(u)

   # u_hat contains the information bits without parity bits and has shape [...,k].
   # crc_valid contains a boolean per codeword that indicates if the CRC validation was successful.
   # It has shape [...,1].
   u_hat, crc_valid = decoder(c)