This graduate course provides an in-depth treatment of modern error correction codes and decoding algorithms.

Error correcting codes (ECC) are an integral part of modern day communications, computer and data storage systems and play a vital role in ensuring he integrity of data in the presence of errors. In the most general terms, the purpose of error correcting code is to protect user data, and this is achieved by appending redundant, so called parity bits, along with the data bits. Low-density parity-check (LDPC) codes are a class of error-correction codes that have revolutionized communications and data storage industry. They have been the focus of intense research over more than a decade because they can approach theoretical limits of reliable transmission over various communications and storage channels even when decoded by sub-optimal low complexity iterative algorithms. The past decade in information theory has been marked by the quest for low complexity decoders, and the emergence of iterative message passing decoders.

Efficient and high-speed implementations coupled with recent advances in integrated circuit technologies, have made LDPC codes de-facto industry standards in a number of systems. With emerging technologies requiring much faster processing speeds with stricter energy utilization constraints while still requiring very low target error-rates, there has been an increasing need for reduced-complexity iterative decoders that provide improved performance.

Wireless networks, satellite communications, deep-space communications, power line communications are among applications where the LDPC codes are the standardized ECC scheme. More specifically LDPC codes are used as an error correcting scheme in: digital video broadcast over satellite (DVB-S2 Standard) and over cable (DVB-C2 Standard), terrestrial television broadcasting (DVB-T2, DVB-T2-Lite Standards), GEO-Mobile Radio (GMR) satellite telephony (GMR-1 Standard), local and metropolitan area networks (LAN/MAN) (IEEE 802.11 (WiFi)), wireless personal area networks (WPAN) (IEEE 802.15.3c (60 GHz PHY)), wireless local and metropolitan area networks (WLAN/WMAN) (IEEE 802.16 (Mobile WiMAX), near-earth and deep space communications (CCSDS), wire and power line communications ( ITU-T G.hn (G.9960)), ultra-wide band technologies (WiMedia 1.5 UWB), etc. [11]. Very recently LDPC codes have found their way in magnetic hard disk drives and optical communications, and they are the main candidates for ECC system in ash memories.

Enrollment Requirements

Course Texts

• Tom Richardson and Ruediger Urbanke, Modern Coding Theory
• S. Lin and W. Ryan, Channel Codes: Classical and Modern
• D.J.C. Mackay, Information Theory, Inference & Learning Algorithms
• M.I. Jordan, An Introduction to Probabilistic Graphical Models

Course Links

Assessment

• Homework: assigned but not graded
• 1-2 projects
• Exams: 2 midterm exams, 1 final exam
• Typical grading policy: 30% midterms, 35% final exam, 15% homework, 20% project

This course is a self-contained introduction to quantum information, quantum computation, and quantum error-correction. The course starts with basic principles of quantum mechanics including state vectors, operators, density operators, measurements, and dynamics of a quantum system. The course continues with fundamental principles of quantum computation, quantum gates, quantum algorithms, and quantum teleportation. A significant amount of time has been spent on quantum error correction codes (QECCs), in particular on stabilizer codes, Calderbank-Shor-Steane (CSS) codes, quantum low-density parity-check (LDPC) codes, subsystem codes (also known as operator-QECCs), topological codes and entanglement-assisted QECCs. The next topic in the course is devoted to the fault-tolerant QECC and fault-tolerant quantum computing. The course continues with quantum information theory. The next part of the course is spent investigating physical realizations of quantum computers, encoders and decoders; including photonic quantum realization, cavity quantum electrodynamics, and ion traps. The course concludes with quantum key distribution (QKD).

The course should alternate with ECE 638: Wireless Communications.

Enrollment Requirements

Course Texts

I.B. Djordjevic, Quantum Information Processing and Quantum Error Correction. Elsevier/Academic Press, 2012.

Summary

This course offers in-depth exposition on the design and realization of a quantum information processing and quantum error correction. The successful student will be ready for further study in this area, and will be prepared to perform independent research. The student completed the course will be able design the information processing circuits, stabilizer codes, CSS codes, subsystem codes, topological codes and entanglement-assisted quantum error correction codes; and propose corresponding physical implementation. The student completed the course will be proficient in fault-tolerant design as well.

Assessment

Homework will be assigned approximately every two weeks.  

Typical grading policy: 20% homework, 30% project, 15% midterm exam, 35% final exam.

This course covers the process of technology development in the photonics industry, both from the perspective of formal processes and case studies. Key aspects of the commercialization process including intellectual property, new product development processes, technical marketing and team building are treated in an interactive program informed by the instructor's 15 years of industry experience in both large corporate R&D organizations and entrepreneurial startups. Graduate-level requirements include completing an executive summary of their business plan/invention disclosure project that is a portion of the Group Gate 2 presentation grade.

The purpose of the course is to give students a comprehensive introduction to free-space optical communication principles. This course offers in-depth exposition on propagation effects in free-space, both outdoor and indoor as well as deep-space; channel impairments in these media including atmospheric turbulence effects and scattering effects; noise sources, channel capacity studies, advanced modulation and multiplexing techniques for free-space applications, advanced detection, and channel compensation techniques; diversity techniques, MIMO techniques, adaptive optics techniques to deal with atmospheric turbulence effects; advanced coding and coded modulation techniques; software-defined free-space optical communications, physical-layer security, and quantum free-space optical communications.

Course Texts

Reference Textbooks (not required) are:

1. C. Andrews, R. L. Philips, Laser Beam Propagation through Random Media, 2nd Ed. SPIE Press, Bellingham, Washington, USA, 2005.
2. I. B. Djordjevic, Advanced Optical and Wireless Communications Systems, Springer, Dec. 2017/Jan. 2018.

Schedule

The purpose of the course is to give students a comprehensive introduction to digital communication principles. The major part of the course is devoted to studying how to translate information into a digital signal to be transmitted, and how to retrieve the information back from the received signal in the presence of noise and intersymbol interference (ISI).

Various digital modulation schemes are discussed through the concept of signal space. Analytical and simulation models for digital modulation systems are designed and implemented in the presence of noise and ISI. Optimal receiver models for digital base-band and band-pass modulation schemes are covered in detail.

Graduate work will include more challenging problem sets and exam problems, and a C/C++ simulation project.

Enrollment Requirements

Course Texts

S. Haykin, Digital Communication Systems. Wiley, 1st edition, 2014.

Schedule

Assessment

• Homework: ~10 problem sets
• Exams: 2 in-class exam, 1 mandatory final exam
• Computer usage: C/C++ exercises
• Contribution to professional component:
  • Math and basic science: 0.5 units
  • Engineering topics: 2 units
  • Significant design experience: 0.5 units

Topics to be selected from opto-electronics, wave guides, non-linear optics, nano-materials and semiconductor materials.

Probability, random variables, stochastic processes, correlation functions and spectra with applications to communications, control and computers.