LP decoding of expander codes: a simpler proof

A code C ⊆ Fn 2 is a (c, ǫ, δ)-expander code if it has a Tanner graph, where every variable node has degree c, and every subset of variable nodes L0 such that |L0| ≤ δn has at least ǫc|L0| neighbors. Feldman et al. (IEEE IT, 2007) proved that LP decoding corrects 3ǫ−2 2ǫ−1 · (δn − 1) errors of (c, ǫ, δ)expander code, where ǫ > 2 3 + 1 3c . In this paper, we provide a simpler proof of their result and show that this result holds for every expansion parameter ǫ > 2 3 .