EE5848 Topics in Information Theory and Coding (July-Nov 2025)

This edition of EE5848 will be an introduction to quantum error correcting codes.

Logistics

Number of credits: 2
Timeslot: F
Segments: 3–6
Classroom: A221 (Academic Block A)

Prerequisites

Students must have credited a 3-credit course on linear algebra or matrix theory; a thorough understanding of matrix theory is essential (especially, trace, inner product, orthogonality, properties of unitary and Hermitian matrices, eigen decomposition, positive semi-definiteness, projection operation and singular value decomposition). Students must be comfortable with the basics of probability theory and random variables. No background in quantum mechanics will be assumed.

It will be helpful for the students to credit the course EE5350 Error Correcting Codes (offered by Dr Myna Vajha in slot D, segments 1–6, July-Nov 2025) to become familiar with the idea of error correction in the classical setting. However, this is not a pre-requisite for EE5848; this course will be self-contained for anyone with a good background in matrix theory.

Course Contents

Basics of Quantum Information: quantum states and density operators; reduction of quantum states via partial trace; projective measurements; characterization of quantum channels; the Kraus representation of quantum channels.

Quantum Noise and Error Correction: Examples of single and multi-qubit quantum channels and errors; Examples of quantum error correction: the 3-qubit code and the Shor code; the Knill-Laflamme conditions for quantum error correction; discretization of errors; minimum distance of a code.

Stabilizer Codes: The Pauli group; definition and properties of stabilizer codes; distance and size of stabilizer codes; sets of detectable and correctable error patterns, minimum distance; symplectic representation of Paulis; CSS codes.

References

Books

Video Lectures

Information Theory, Coding and Inference (Jan-May 2025)

This course will serve as an introduction to information theory and will highlight its connections to statistics and coding via the following problems: binary hypothesis testing, data compression, and coding for noisy channels.

The primary references for this course are

  • Thomas Cover and Joy Thomas, Elements of Information Theory, Second Edition, Wiley-Interscience
  • Yury Polyanskiy and Yihong Wu, Information Theory: From Coding to Learning, draft available at Yury Polyanskiy’s page.

Linear Systems and Signal Processing (Jul-Dec 2024)

This course is an introduction to Fourier domain techniques for analysing continuous-time and discret-time signals and linear time-invariant (LTI) systems. The following topics will be covered: Fourier series, Fourier transform (continuous- and discrete-time), Discrete Fourier Transform, LTI systems, and (if time permits) Laplace and Z-transforms.

The lectures will be based on the following references

Other Recent Courses

Matrix Theory (Aug-Dec 2023).