Laurent Schmalen's short lecture at the 2020 European School of Information Theory Stuttgart, Germany
In this lecture, we will review spatially coupled LDPC codes, one of the few classes of codes that are universally capacity achieving over a broad range of channels. We review basic construction methods and show the main convergence behavior. We highlight how to construct codes tailored to this specific convergence behavior that significantly outperform LDPC codes, even at very low bit error rates. This makes this class of codes well suited for applications that require extremely low error rates like optical communications or data storage. In the second part of the lecture, we show that spatially coupled LDPC codes have outstanding burst correction properties that make them well suited for channels with burst errors and distributed storage applications (where the outage of a server can be modeled as a burst erasure). We show how to calculate bounds on the correction performance and how to use these to design codes.