A wireless communication network, comprising: a base station; and a plurality of user equipments for non-orthogonally transmitting data to the base station, each user equipment comprising at least one antenna, a user-equipment-specific codebook including a plurality of codewords, each codeword being a vector including a plurality of symbols, each symbol to be transmitted over resources of the wireless communication network, an encoder configured to receive an information message to be transmitted to the base station, to select from the codebook the codeword associated with the received information message, and to divide the selected codeword into a plurality of sub-codewords, and a transceiver coupled to the encoder and to the at least one antenna, the transceiver configured to transmit initially via the at least one antenna only a first sub-codeword, and to transmit via the at least one antenna a second sub-codeword responsive to an indication that the encoded information message was not successfully decoded at the base station only on the basis of the received first sub-codeword and based on compressed sensing, wherein the resources of the wireless communication network includes a plurality of resource elements, wherein at least a subset of the plurality of resource elements is shared by the plurality of user equipments (UEs) for transmitting data from the plurality of user equipments (UEs) to the base station, and wherein the symbols of the vector representing a codeword are transmitted over the shared resource elements of the wireless communication network and wherein the signals from the plurality of user equipments are multiplexed and transmitted to the base station over shared resources of the wireless communication network; wherein the transceiver is configured to stop transmitting the second sub-codeword responsive to an acknowledgement from the base station, the acknowledgement indicating that the encoded information message was successfully decoded at the base station on the basis of the received first sub-codeword, and the transceiver is configured to transmit the second sub-codeword in case no acknowledgement is received from the base station. a base station; and a plurality of user equipments for non-orthogonally transmitting data to the base station, each user equipment comprising at least one antenna, a user-equipment-specific codebook including a plurality of codewords, each codeword being a vector including a plurality of symbols, each symbol to be transmitted over resources of the wireless communication network, an encoder configured to receive an information message to be transmitted to the base station, to select from the codebook the codeword associated with the received information message, and to divide the selected codeword into a plurality of sub-codewords, and to receive an information message to be transmitted to the base station, to select from the codebook the codeword associated with the received information message, and to divide the selected codeword into a plurality of sub-codewords, and a transceiver coupled to the encoder and to the at least one antenna, the transceiver configured to transmit initially via the at least one antenna only a first sub-codeword, and to transmit via the at least one antenna a second sub-codeword responsive to an indication that the encoded information message was not successfully decoded at the base station only on the basis of the received first sub-codeword and based on compressed sensing, to transmit initially via the at least one antenna only a first sub-codeword, and to transmit via the at least one antenna a second sub-codeword responsive to an indication that the encoded information message was not successfully decoded at the base station only on the basis of the received first sub-codeword and based on compressed sensing, wherein the resources of the wireless communication network includes a plurality of resource elements, wherein at least a subset of the plurality of resource elements is shared by the plurality of user equipments (UEs) for transmitting data from the plurality of user equipments (UEs) to the base station, and wherein the symbols of the vector representing a codeword are transmitted over the shared resource elements of the wireless communication network and wherein the signals from the plurality of user equipments are multiplexed and transmitted to the base station over shared resources of the wireless communication network; wherein the transceiver is configured to stop transmitting the second sub-codeword responsive to an acknowledgement from the base station, the acknowledgement indicating that the encoded information message was successfully decoded at the base station on the basis of the received first sub-codeword, and the transceiver is configured to transmit the second sub-codeword in case no acknowledgement is received from the base station.