A class of quantum LDPC codes: construction and performances under iterative decoding

A generic method for constructing quantum LDPC codes is presented. We first explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Our approach is based on a graph representation of the generators of the stabilizer group and on a simple local rule to ensure commutativity. We provide several specific examples of quantum LDPC codes obtained by our method, together with numerical simulations over the depolarizing channel and the erasure channel.