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Started writing the introduction

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Marius Drechsler 2024-08-20 21:20:31 +02:00
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#import "@preview/glossarium:0.4.1": *
= Introduction
These are the introducing words
#gls("puf", display: "Physical unclonable functions (PUF)")
== Notation
To ensure a consistent notation of functions and ideas, we will now introduce some required conventions
To ensure a consistent notation of functions and ideas, we will now introduce some conventions
Random distributed variables will be notated with a capital letter, i.e. $X$, its realization will be the corresponding lower case letter, $x$.
Vectors will be written in bold text: $bold(k)$ represents a vector of quantized symbols.
Matrices are denoted with a bold capital letter: $bold(M)$
We will call a quantized symbol $k$. $k$ consists of all possible binary symbols, i.e. $0, 01, 110$.
A quantizer will be defined as a function $cal(Q)(x, bold(a))$ that returns a quantized symbol $k$.
We also define the following special quantizers for metric based HDAs:
A quantizer used during the enrollment phase is defined by a calligraphic $cal(E)$.
For the reconstruction phase, a quantizer will be defined by a calligraphic $cal(R)$
@example-quantizer shows the curve of a 2-bit quantizer that receives $tilde(x)$ as input. In the case, that the value of $tilde(x)$ equals one of the four bounds, the quantized value is chosen randomly from the relevant bins.
#figure(