Beam-space time coding methods are being extensively investigated, since they provide levels of performance appropriate for the next and future generations of wireless communication systems. In this paper, we focus on beam-domain space-time coding, especially considering the case when transmit beams have inter-beam interference (IBI). A new beam-space time coding scheme that takes into account the overlap amount among beams is proposed. We observe that the overlap of beams introduces an amount of correlation to the channels in a similar way to the well-known Partial Response (PR) channel in magnetic recording. Based on that observation, the proposed system can make use of IBI to encode and decode the signals. We evaluate the proposed system both via theoretical upper bound and via computer simulations. The Bit Error Rate (BER) performance of the proposed system using IBI is better than that of the system with no-IBI because the proposed system delivers more coding gain. However, the overlap of beams decreases the diversity gain. The tradeoff relationship between diversity gain and coding gain is investigated.