Simple Constructions of Unique Neighbor Expanders from Error-correcting Codes
CoRR(2023)
摘要
In this note, we give very simple constructions of unique neighbor expander
graphs starting from spectral or combinatorial expander graphs of mild
expansion. These constructions and their analysis are simple variants of the
constructions of LDPC error-correcting codes from expanders, given by
Sipser-Spielman [SS96] (and Tanner [Tan81]), and their analysis. We also show
how to obtain expanders with many unique neighbors using similar ideas.
There were many exciting results on this topic recently, starting with
Asherov-Dinur [AD23] and Hsieh-McKenzie-Mohanty-Paredes [HMMP23], who gave a
similar construction of unique neighbor expander graphs, but using more
sophisticated ingredients (such as almost-Ramanujan graphs) and a more involved
analysis. Subsequent beautiful works of Cohen-Roth-TaShma [CRT23] and Golowich
[Gol23] gave even stronger objects (lossless expanders), but also using
sophisticated ingredients.
The main contribution of this work is that we get much more elementary
constructions of unique neighbor expanders and with a simpler analysis.
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关键词
unique neighbor expanders,simple constructions,codes,error-correcting
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