Classes

This course will educate a cohort of engineers capable of selecting, designing, and deploying erasure and error-correcting codes suitable for current and forthcoming technologies to make new networks that are reliable, fast, efficient, and fit for modern purposes.

In our data-driven world, the storage and transport of digital information is a key component underpinning all technologies. Low-latency, high-fidelity access to information is central to enabling algorithms that impact how we work, are entertaining, travel, and, indeed, our healthcare.

Yet all digital data is potentially subject to corruption when stored or communicated, which can have damaging consequences. Erasure and error-correcting codes are widely deployed to enable the accurate recovery of information. Still, new applications, including distributed storage, AR/VR, and V2X, are placing previously unforeseen demands, requiring further innovation to create reliable networks that fit contemporary requirements.

Course Description

During this course you will learn:

• The demands of new applications.
• Recent innovations in coding.
• How erasure and error correction codes and decoders are designed and how they work. How to create software implementations of encoders and decoders to rectify corrupted data.

Course Contents

• The course introduces modern approaches to ensuring reliable network communication and storage, covering theory and use cases. 
• After an accessible, engineering-centric introduction to Galois fields, we present erasure coding and decoding, with applications to coding-based protocols that reduce delays over links and networks (network coding), post-quantum security, and speed-up of distributed computation. 

• The second part considers error correction, starting with a brief overview of channel capacity. We begin with hard detection, as in storage systems.
• We introduce common codes and decoding using guessing random additive noise decoding (GRAND), which can decode any code. 
• We generalize to using detector-generated information (soft information) and show how GRAND can be extended to soft information systems, with examples such as CA-Polar decoding. 
• We discuss hardware implementation and realization in silicon.

Pre-Requisites

There are no formal prerequisites, but familiarity with linear algebra and probability is essential, as is familiarity with MATLAB, Python, or equivalent. Reach out to the instructor if you are unsure you meet the requirements.

Course Grading

The grades will be:

• 12% per homework (total 60%).
• Final project 30%.
• Class participation 10%.