Error correcting codes and spatial coupling
Rafah El-Khatib, Jean Barbier, Ayaka Sakata, and R\"udiger Urbanke
TL;DR
This paper discusses the fundamentals of polar and low-density parity-check codes and explores how spatial coupling enhances belief propagation decoding, based on lecture notes from a 2013 school.
Contribution
It provides an overview of error correcting codes and demonstrates the benefits of spatial coupling in improving decoding performance.
Findings
Spatial coupling improves belief propagation decoding.
Basics of polar and LDPC codes are explained.
Spatial coupling enhances error correction capabilities.
Abstract
These are notes from the lecture of R\"udiger Urbanke given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches, France from Monday September 30th, 2013, till Friday October 11th, 2013. The school was organized by Florent Krzakala from UPMC and ENS Paris, Federico Ricci-Tersenghi from La Sapienza Roma, Lenka Zdeborov\`a from CEA Saclay and CNRS, and Riccardo Zecchina from Politecnico Torino. The first three sections cover the basics of polar codes and low density parity check codes. In the last three sections, we see how the spatial coupling helps belief propagation decoding.
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Taxonomy
TopicsError Correcting Code Techniques · Advanced Wireless Communication Techniques · DNA and Biological Computing