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Performance of wireless communications systems is degraded by fading, typically combated via spatial diversity by multiple transmit and receiver antennas. Practical limitations may limit their use; thus, cooperative transmissions have been proposed to introduce diversity without the need for multiple antennas. We propose a novel cooperative scheme that performs distributed coding of user data. It needs each user transmit on one single channel and allows large flexibility between rate and diversity. A trade-off is increased complexity as more users are required to be decoded simultaneously by the base station. We present construction of the distributed code for different choices of rates and diversity orders by means of simple linear block codes, resulting in reduced complexity for decoding operations. Achieved diversity order is bounded by the minimum distance of the implemented distributed code. Performance of the scheme is studied via analytical bounds and numerical simulations.