FYP Project I: Channel Polarization: A General Phenomenon Why Coding Works

1. FYP Project I: Channel Polarization: A General Phenomenon Why Coding Works Prof. Xiaojun Yuan Presenter: Prof. Angela Yingjun Zhang

2. Polar Codes: A Brief Overview • Polar codes • invented by Erdal Arıkan in 2007 • Provides a new paradigm for coding • Properties of polar codes • Elegant coding structure • Provable capacity achievability • Low complexity • Many applications 2

3. Channel Polarization A bit from a noisy channel with capacity in (0, 1) Synthesizing A bit from a channel with capacity = 1 A bit from a channel with capacity = 0 To synthesize, out of N independent copies of a binary-input channel, a different set of N binary-input noisy channels, such that the capacities of the latter set, except for a negligible fraction of them, are either near 1 or near 0. 3

4. Project Targets • The goal of this project is to understand themechanism of channel polarization and to simulate polar codes. • Specific targets include: • Read the original paper by Aricon and understand themechanism of channel polarization; • Understand the modeling for various communication channels, such as erasure channels, additivewhite Gaussian noise (AWGN) channels, etc. • Simulate polar codes over physical channels (such as binaryerasure channels, binary AWGN channels, etc) using C++or Matlab; • *Explore the possibility of improving polar codes (with afaster decoding algorithm, a faster convergence speed, etc). *Not mandatory

5. Required Skills • Good mathematical skills • Good programming skills • Matlab and/or C++ • Good English reading and writing skills • Number of students to be involved: • <= 2 5