Short Courses

Error-control coding, the technique of adding redundancy in controlled fashion to transmitted data so as to correct errors introduced by noise or other channel impairments, is a key component of modern optical communication systems. This course introduces basic concepts in coding and information theory: channel models and channel capacity (the Shannon limit), with an emphasis of optical channel characteristics important for FEC. Encoders and decoders (hard-decision and soft-decision), linear block codes, code rate and overhead, Hamming distance, net coding gain, generator matrices, parity-check matrices, and syndromes. Specific families and constructions of error-correcting codes will be described, including single parity check-, Reed-Muller-, Hamming-, Reed-Solomon-, and BCH codes. These basic concepts are then extended to more advanced product and product-like codes like the OFEC code used in recent optical transceivers. An overview over the FEC landscape in optical communication is provided. The course material is complemented by python code offering the participant hands-on experience in FEC analysis.

This course should enable participants to:

* Define the key parameters of an error-correcting code.
* Explain the system-level benefits provided by FEC.
* Discuss the existence of fundamental limits (Shannon capacity) on FEC.
* State the optical channel properties important for FEC.
* Interpret generator-matrix and parity-check-matrix descriptions of a code.
* Encode and decode a binary Hamming code.
* Describe the key parameters of binary BCH codes.
* Interpret the properties of FEC codes used in optical communications like, e.g., the OFEC code.

Georg Böcherer holds M.Sc. (ETH Zürich, 2007), Ph.D. (RWTH Aachen University, 2012), and Dr.-Ing. habil. (Technical University of Munich (TUM), 2017) degrees, all in electrical engineering. 2017-2020, he worked as senior engineer at the Optical Communication Technology Lab of Huawei Technologies France, and since 2020, we works as principal engineer at the Optical and Quantum Communications Lab of Huawei Technologies Germany. Since 2018, he is lecturer at the TUM. His research is on machine learning, forward error correction, DSP, and information theory. G. Böcherer is the inventor of Probabilistic Amplitude Shaping. He received a Bell Labs Prize in 2015, the Johann-Philipp-Reis-Preis in 2017 and the 2019 IEEE/OSA JLT best paper award in 2019.