Tutorial 1: Quantum LDPC codes
Given by: Anthony Leverrier, INRIA
The prospect of building a large-scale quantum computer is of great interest to the fields of quantum error correction and quantum fault tolerance. Perhaps the most salient distinction between classical and quantum coding is that the latter is concerned with two types of errors (bit flipping and phase flipping). In fact, most quantum codes are built from two classical codes C_1 and C_2: one for each type of error. The main difficulty is that the two codes cannot be chosen arbitrarily, and must be such that C_1 contains the dual of C_2. In particular, it is non trivial to satisfy this condition for quantum LDPC codes, i.e. when C_1 and C_2 are both LDPC, if one wants to achieve good code parameters.
Since the LDPC property is extremely useful for implementations, much work has been devoted to designing codes with good parameters and efficient decoding algorithms. In particular, it has taken more than 20 years to prove quantum LDPC codes with distance scaling better than the square root of the code length.
The goal of this tutorial is to first recall the basics of quantum coding and the most studied quantum LDPC code: the toric code. I will then explain the recent construction of quantum Tanner codes, which form an asymptotically good family of quantum LDPC codes. This construction is strongly inspired by the expander codes of Sipser and Spielman, and can be understood even without any prior exposure to quantum coding. I will conclude with a list of open questions in the field.
Anthony Leverrier is a quantum information theorist at Inria Paris. He received a PhD in computer science from Telecom ParisTech in 2009 for his work on security proofs for quantum key distribution, and the Habilitation à Diriger des Recherches in 2017 from Université Pierre and Marie Curie in Paris. After postdoctoral positions at ICFO Barcelona and ETH Zurich, he joined Inria in 2012. He has published over 50 research articles in physics and computer science on topics ranging from quantum cryptography and quantum foundations to quantum error correcting codes. His research now focuses specifically on quantum Low-Density Parity-Check (LDPC) codes, which have the potential to reduce the overhead required for fault-tolerant quantum computing. In particular, he has contributed to the development of good quantum LDPC codes displaying a finite encoding rate and a linear minimum distance and helped designing efficient decoders for these codes.
Tutorial 2: Recent advances in deep learning for channel coding
Given by: Sebastian Cammerer, NVIDIA
In the recent years, machine learning has become an omnipresent tool for communications research and it is foreseeable that in particular deep learning will play an increasingly important role in the future evolution of 5G as well as the development of 6G. Hence, this tutorial provides an overview of the key concepts and challenges when applying deep learning to channel coding, ranging from weighted belief propagation over graph neural networks (GNN) for decoding, to entirely neural network-based communication systems that implicitly learn new coding schemes. After a short primer on deep learning for communications, we categorize the different recent research directions and distinguish between a model deficit and an algorithm deficit. Further, we introduce the concepts of online, offline and design- time learning and discuss their promises as well as the resulting implications.
The remainder of the tutorial focuses on scalability and shows that it is advantageous to limit the degrees of freedom by imposing carefully selected neural network structures. As an example, we discuss a joint detection and decoding scheme for short-packet wireless communications in scenarios that require to first detect the presence of a message before actually decoding it. Thus, we learn short messages that can be, all « at once », detected, synchronized, equalized and decoded when sent over an unsynchronized channel with memory. The conceptional advantage of the proposed system stems from a holistic message structure with superimposed pilots for joint detection and decoding without the need of relying on a dedicated preamble.
The goal of this tutorial is to enable the attendees to identify potential applications of deep learning in their own research field. For this, we will introduce Sionna, a new open-source software library for GPU- accelerated link-level simulations and 6G research with native support for the integration of neural networks. The attendees will receive detailed Jupyter notebooks with code examples to deepen their understanding and to quickly explore their own research ideas.
Sebastian Cammerer is a Research Scientist at NVIDIA working on the intersection of wireless communications and machine learning. Before joining NVIDIA, he received his PhD in electrical engineering and information technology from the University of Stuttgart, Germany, in 2021. He is one of the maintainers and core developers of the Sionna open-source link-level simulator.
His main research topics are machine learning for wireless communications and channel coding. Further research interests include parallel computing for wireless signal processing and information theory. He is recipient of the VDE ITG Dissertationspreis 2022, the IEEE SPS Young Author Best Paper Award 2019, the Best Paper Award of the University of Stuttgart 2018, and third prize winner of the Nokia Bell Labs Prize 2019.