Mathematical breakthroughs are often made by making the abstract concrete. For example, additive continuous map from R^m to R^n sounds complicated, but m x n matrix sounds a lot better.
In coding theory, there is a similar breakthrough: Traditionally, channel coding is about how to manipulate bits and symbols. However, we can see it as a way to manipulate channels as if channels were concrete objects.
By treating channels as concrete objects, we can study the convergence of a sequence of channels, partial orders on channels, and even distributions on the space of all channels. This viewpoint is proved powerful for design and analysis of polar codes and low-density parity-check (LDPC) codes which achieve Shannon capacity and are the two pillars of the 5G standard.
In this talk, we give an overview of recent advanced results regarding polar and LDPC codes.
This is a 15 minute talk summarizing what I did for my PhD and half of my postdoc research.
For the materials of a one hour talk, check out my jobtalks.