Edge Transitive Ramanujan Graphs and Highly Symmetric LDPC Good Codes
Information Theory
2011-08-16 v1 Combinatorics
Group Theory
math.IT
Abstract
We present a symmetric LDPC code with constant rate and constant distance (i.e. good LDPC code) that its constraint space is generated by the orbit of one constant weight constraint under a group action. Our construction provides the first symmetric LDPC good codes. This solves the main open problem raised by Kaufman and Wigderson in [4].
Cite
@article{arxiv.1108.2960,
title = {Edge Transitive Ramanujan Graphs and Highly Symmetric LDPC Good Codes},
author = {Tali Kaufman and Alexander Lubotzky},
journal= {arXiv preprint arXiv:1108.2960},
year = {2011}
}