LP decoding of codes with expansion parameter above 2/3

Feldman et al. (2007) [3] proved that LP decoding corrects $\frac{3ϵ‐2}{2ϵ‐1}·(dn‐1)$ errors of $(c,\delta ,ϵ)$ ‐expander code, where $ϵ>\frac{2}{3}+\frac{1}{3c}$ . A code $C\subseteq {‐{F}}_2^n$ is a $(c,\delta ,ϵ)$ ‐expander code if it has a Tanner graph, where every variable node has degree c, and every subset of variable nodes $L_0$ such that $|L_0|⩽\delta n$ has at least $ϵc|L_0|$ neighbors. In this paper, we provide a slight consolidation of their work and show that this result holds for every expansion parameter $ϵ>\frac{2}{3}$ .