We　construct　and　implement　a　compressive　sensing　measurement　matrix　based　on　improved　size-compatible　(ISC)-array　low-density　parity-check　(LDPC)　code.　First,　we　propose　an　improved　measurement　matrix　from　the　array　LDPC　code　matrix.　The　proposed　measurement　matrix　retains　suitable　quasi-cyclic　structures　and　supports　arbitrary　code　lengths.　It　also　achieves　a　high　perfect　recovery　percentage　compared　with　a　Gaussian　random　matrix　of　the　same　size.　Second,　we　propose　a　hardware　scheme　using　cycle　shift　registers　to　design　the　compressive　sensing　measurement　matrix　generator.　This　provides　simple　circuit　architecture　during　the　generation　of　the　measurement　matrix.　According　to　simulation　verifications,　the　measurement　matrix　construction　method　is　effective　and　entails　fewer　shift　registers　and　a　lower　area　overhead　by　using　a　simplified　hardware　implementation　scheme.　The　compressive　sensing　measurement　matrix　generator　can　generate　all　of　the　required　elements　in　the　ISC-array　LDPC　code　matrix　with　an　acceptable　hardware　overhead.　Therefore,　it　can　be　widely　applied　to　large-scale　sparse　signal　compressive　sensing.