The Alternate Direction Method of Multipliers (ADMM) approach is an original method for LDPC decoding based on the linear programming (LP) technique. It introduces a novelty at the error correction performance level. Nevertheless, this method can be toughly implemented due to its high computational complexity. In this paper, an implementation of the ADMM LP decoding algorithm on an FPGA target is presented. Its hardware resource cost is evaluated and compared with the state of the art LDPC decoders using the belief propagation (BP) decoding approach. The preliminary logic synthesis results show that an LP based hardware decoder for LDPC codes should be viable for applications with tough error correction requirements. However, additional research works are required to reach equivalent hardware complexity and throughput performances that are similar to traditional BP based LDPC decoders.