# Information Theory

### Coding and Signal Processing For Future Fibre-Optical Communications

**A/Prof. Terence Chan** and **Prof. Alex Grant**

Optical communications offers many advantages compared to its radio frequency counterpart. Optical carriers have a much higher carrier frequency, allowing for significantly higher information bandwidth. Currently, technological advance in optical communications is overwhelmingly driven by breakthroughs in physics and photonics. As photonics technologies mature, and data rates increase, higher-order nonlinear physical effects and dispersion in the medium cannot be ignored (especially for long-haul transmission). Advanced digital coding and signal processing techniques become increasingly relevant to address these channel impairments. The aim of this project is to answer the most basic information theoretic questions concerning data transmission over optical channels. The emphasis is on mathematical foundations informed by sufficiently accurate physical propagation models.

The project will

- Develop the information theoretic tools required for analysis of nonlinear optical channels
- Determine the fundamental limits imposed by physics on information transmission over fibre channels
- Develop new information theoretically optimal coding and modulation techniques for optical communications

### Information theoretic security and privacy

Information theoretic security relies on no assumption on the computational power of the adversary. Since the seminal work by Shannon in 1949, a lot of important results have been developed. Recently, we have a breakthrough by showing a new fundamental relationship between key size and message size. A new concept about the consumption of a secret key has been developed.

This project explores other fundamental questions in this new direction. The results can be applied to security problems and also the protection of privacy when we use the Internet.

### Refinement of fundamental tools in information theory

In information theory, many famous tools or results cannot be applied to countably infinite alphabets, e.g., strong typicality, Fano’s inequality and one-time pad. It is important to consider countably infinite alphabets because this is the general case and this usually gives tighter bounds, faster convergent rates, etc. Recently, we have generalized the aforementioned tools to countably infinite alphabets due to the observation that entropy is indeed a discontinuous function.This project aims to generalize more fundamental results in information theory. Students with good mathematical and analytical skills are preferred.

### Network information theory

Information theory (or Shannon Theory) is the mathematical study of information transmission, processing and utilisation. An overarching goal of this theory is to determine exactly how much information can be (or should be) transmitted in a telecommunications network. Information theorists formally referred to this goal as: "the characterisation of the admissible rate region of a network."

Over the past half century, information theory has been tremendously successful in characterizing admissible rates for point-to-point telecommunication networks involving one transmitter and one receiver. Unfortunately, the theory appears to be ill-equipped for telecommunication networks with multiple users. A unified theory to study the problems of multi-user information theory is yet to be realised. This project is devoted to the formalisation and characterisation of new notions of admissible rate regions of longstanding open multi-user network problems and the collective tools required to attain them.

### Partial rate region characterisations: new frontiers of information theory

**Dr Siu-Wai Ho** and **Dr Badri N. Vellambi**

Rate regions define the fundamental limits of applications in different areas, including data networks, wireless communications, and security systems. However, techniques of information theory are unable to completely characterise these regions for every application. Our aim is to develop methods for analysing rate regions that do not rely on complete characterisations. These methods will revolutionise our understanding of rate regions by bypassing the difficulties of existing techniques.

Outcomes will provide practically relevant properties of rate regions that will enable novel applications in communications systems.