Forward Error Correction (FEC)

The forward error correction (FEC) package provides encoding and decodingalgorithms 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 decodingalgorithms are mostly general and can be used in combination with othercode designs.

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

The following figure shows the evolution of FEC codes from GSM (2G) up to the5G NR wireless communication standard. The different codes are simulated withthe Sionna FEC package for two different codeword length of\(n=1024\)(coderate\(r=1/2\)) and\(n=6156\) (coderate\(r=1/3\)),respectively.

Remark: The performance of different coding scheme varies significantly withthe choice of the exact code and decoding parameters which can befound in the notebookFrom GSM to 5G - The Evolution of Forward ErrorCorrection. Further, the situation alsochanges for short length codes and results can be found in5G Channel Coding:Polar vs. LDPC Codes.

../../_images/FEC_evolution.png

Please note that thebest choice of a coding scheme for a specific applicationdepends 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.

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