Expander code: Difference between revisions

Revision as of 09:10, 25 December 2023

Latest revision as of 06:40, 22 July 2024

Line 20:

==Expander codes==

In [[coding theory]], an expander code is a <math>[n,n-m]_2\,</math> [[linear block code]] whose parity check matrix is the adjacency matrix of a bipartite [[expander graph]]. These codes have good relative [[Block code#The distance d|distance]] <math>2(1-\varepsilon)\gamma\,</math>, where <math>\varepsilon\,</math> and <math>\gamma\,</math> are properties of the expander graph as defined later), [[Block code#The rate R|rate]] <math>\left(1-\tfrac{m}{n}\right)\,</math>, and decodability (algorithms of running time <math>O(n)\,</math> exist).

==Definition==