IZS 2024 Plenaries

On Convex Hulls and the (Im)Possibility of Overparametrization

Sara van de Geer (ETH Zurich)

Abstract: We review known bounds for the entropy of a class of functions ℱ formed by taking the convex hull of a class with polynomial covering numbers. These entropies are relatively small: the class ℱ is not “overparametrized”. More generally, we consider the convex hull of a class with polynomial approximation numbers. Given N ∈ ℕ, the N-approximation number of a class of functions is the approximation error of its best N-dimensional linear approximation. We examine the case where this error is of order N^(−1/W) for some given W > 0. We briefly discuss some related literature where entropy bounds are based on small ball estimates. As illustration, we look at the space of functions on ℝ^d with bounded (higher order) Vitali total variation, and apply the results to tensor denoising.

Slides (PDF)

Physical Unclonable Functions: Coded Modulation, Shaping, and Helper Data Schemes

Robert F. H. Fischer (Ulm University)

Abstract: Physical unclonable functions (PUFs) generate fingerprints by exploiting randomness that intrinsically occurs in integrated circuits due to uncontrollable variations in the manufacturing process of physical objects. Most of the literature deals with binary PUFs and employ binary hard-decision decoding to stabilize the response against environmental variations and readout errors.

It is of interest to i) increase the reliability by employing soft-decision decoding and ii) increase the size of the extracted key by resorting to higher-order alphabet or, even better, by applying methods from coded modulation and signal shaping.

In this talk, a suited model for studying PUFs with real-valued readout is presented. The transition from binary PUFs to schemes utilizing coded modulation and signal shaping will be discussed. The main item in PUFs is the so-called helper data scheme, which in the first place enables decoding. Suited schemes are presented and it is shown how the helper data, which has to be independent of the PUF readout, can be designed to improve decodability.

Slides (PDF)

Networks and Helpers

Yossef Steinberg (Technion – Israel Institute of Technology)

Abstract: It has long been observed that cooperation in communication networks can significantly enhance the network performance. Cooperation can take place in many forms: conference links between users, helpers that send to the users information on the channel state, feedback links that enable message sharing between users, and more. Each of these forms require system resources - dedicated time slots, bandwidth, energy, computational power etc. Unfortunately, in modern communication networks, these resources cannot be guaranteed a-priori: users that serve as helpers come and go, their willingness to serve others' communication needs may depend on battery status, mobility, and other parameters that cannot be predicted before communication begins. Moreover, often active users cannot be notified about missing system resources, thus coding schemes cannot be dynamically updated according to system state. Hence there is a need for robust coding schemes, that utilize cooperation resources when they exist, but can operate also when they are absent, possibly at reduced decoding rates. Naturally, robustness does cost something — the resulting rates would be lower than the achievable rates when the system state (resources) is stable and known a priori to all.

In this talk I will present basic cooperation/helpers models. I will discuss situations where users cannot be notified about the availability of conference links or helpers, thus requiring robust schemes. Bounds and capacity results will be presented for a few central models.

Slides (PDF)

These videos can also be found at the video portal of ETH Zurich.

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