Multiple antenna systems are promising approaches to increase the data rate of wireless communication systems. There, modulated symbols are multiplexed on multiple transmission antennas. Typically an outer error correcting code is used additionally to ensure a desired quality of service for a given data rate. An appropriate communications performance can be achieved by iterative decoding, where probabilistic information are exchanged between outer decoder and the MIMO demodulator. However, in this case the MIMO demodulator has to calculate probabilistic soft-output values for each bit which can be very complex. In this paper we present a new class of linear block codes named low-density MIMO codes which reduces the complexity of the MIMO soft-demodulator and the outer channel decoder inherently by code design without decreasing the data rate of the overall system. These LDMC codes can have a better communications performance then state of the art solutions with a order of magnitude smaller decoding complexity.