Advanced & Applied Topics · Information Theory & Entropy

Information theory: communication channels and channel capacity

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Probabilistic, Algebraic and Advanced Mathematical Analysis

Overview

Topics covered

  • Introduction
  • Information Theory: Communication Channels and Capacity
  • Historical perspective and Shannon's paradigm
  • Mathematical foundations and measurement spaces
  • 1. Shannon entropy
  • 2. Joint and Conditional Entropy

Related concepts

Main connections

  • Calculus & differentiation
  • Linear algebra & matrices
  • Normal (Gaussian) distribution
  • Permutation & exact tests
  • Variance & standard deviation
  • Mean & expected value

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

H(X)=−∑x∈𝒳p(x)logbp(x)=𝔼[logb1p(X)]
View LaTeX sourceH(X) = -\sum_{x \in \mathcal{X}} p(x) \log_b p(x) = \mathbb{E}\left[\log_b \frac{1}{p(X)}\right]