The　protograph　low-density　parity-check　(LDPC)　codes　possess　many　attractive　properties,　such　as　the　low　encoding/decoding　complexity　and　better　error　floor　performance,　and　hence　have　been　successfully　applied　to　different　types　of　communication　and　data　storage　channels.　In　this　study,　the　authors　design　protograph　LDPC　codes　for　communication　systems　corrupted　by　the　impulsive　noise,　which　are　modelled　as　additive　white　symmetric　alpha-stable　noise　(AWS$\alpha　$alpha　SN)　channels.　They　start　by　presenting　a　novel　simulation-based　protograph　extrinsic　information　transfer　analysis　to　derive　the　iterative　decoding　threshold　of　the　protograph　codes.　By　further　applying　the　asymptotic　weight　distribution　analysis,　the　authors　design　new　protograph　codes　for　the　AWS$\alpha　$alpha　SN　channel.　Both　theoretical　analysis　and　simulation　results　demonstrate　that　the　proposed　protograph　codes　can　provide　better　error　rate　performance　than　the　prior　art　AR4JA　code,　the　irregular　codes　optimised　for　the　AWGN　channel,　as　well　as　the　irregular　codes　optimised　for　the　AWS$\alpha　$alpha　SN　channel.