# Advanced topics in information theory

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## Contents

Calendar: Summer 2009 Venue: LUMS School of Science & Engineering Organizer: Abubakr Muhammad

This group meets every week at LUMS to discuss some advanced topics in information theory.

## Participants

• Mubasher Beg
• Shahida Jabeem
• Qasim Maqbool
• Hassan Mohy-ud-Din
• Zartash Uzmi
• Shahab Baqai

## Topics

• Rate distortion theory
• Network information theory
• Kolmogorov complexity
• Quantum information theory

## Sessions

### July 7: Organization. Recap of CS-683

• Basic organization, presentation assignments.
• Review of Information theory ideas
• Entropy, AEP, Compression and Capacity

Entropy of a random variable is given by

$H(X) = -\sum_{x \in \mathcal{X}} p(x) \log p(x).$

The capacity of a channel is defined by

$\mathcal{C} = \max_{p(x)} I(X; Y).$

Compression and Capacity determine the two fundamental information theoretic limits of data transmission, $H \leq R \leq \mathcal{C}.$

• A review of Gaussain channels and their capacities.
• Let us take these analysis one step further. How much do you loose when you cross these barriers?
• We saw one situation when you try to transmit over the capacity. By Fano's inequality

$P_e \geq 1 - \frac{C}{R} - \frac{1}{nR}$

• Rate distortion: A theory for lossy data compression.