Forward Error Correction (FEC)
==============================

The forward error correction (FEC) package provides encoding and decoding
algorithms for several coding schemes such as low-density parity-check (LDPC),
Polar, Turbo, and convolutional codes as well as cyclic redundancy checks (CRC).

Although LDPC and Polar codes are 5G compliant, the decoding
algorithms are mostly general and can be used in combination with other
code designs.

Besides the encoding/decoding algorithms, this package also provides
interleavers, scramblers, and rate-matching for seamless integration of the FEC
package into the remaining physical layer processing chain.

The following figure shows the evolution of FEC codes from GSM (2G) up to the
5G NR wireless communication standard. The different codes are simulated with
the Sionna FEC package for two different codeword length of :math:`n=1024`
(coderate :math:`r=1/2`) and :math:`n=6156` (coderate :math:`r=1/3`),
respectively.

*Remark*: The performance of different coding scheme varies significantly with
the choice of the exact code and decoding parameters which can be
found in the notebook `From GSM to 5G - The Evolution of Forward Error
Correction <../../tutorials/notebooks/Evolution_of_FEC.ipynb>`_. Further, the situation also
changes for short length codes and results can be found in `5G Channel Coding:
Polar vs. LDPC Codes <../../tutorials/notebooks/5G_Channel_Coding_Polar_vs_LDPC_Codes.ipynb>`_. 

.. figure:: ../../figures/FEC_evolution.png
   :align: center

Please note that the *best* choice of a coding scheme for a specific application
depends on many other criteria than just its error rate performance:

- Decoding complexity, latency, and scalability
- Level of parallelism of the decoding algorithm and memory access patterns
- Error-floor behavior
- Rate adaptivity and flexibility

All this--and much more--can be explored within the Sionna PHY FEC module.

.. toctree::
   :hidden:
   :maxdepth: 5

   fec.linear
   ldpc/index
   polar/index
   conv/index
   turbo/index
   fec.crc
   fec.interleaving
   fec.scrambling
   utils/index