| CPC H04W 74/0833 (2013.01) | 20 Claims |

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1. A transmitting device for a random-access communication, comprising:
an encoder that is configured to:
acquire an input message having a sequence of bits;
form a plurality of blocks from the sequence of bits; and
determine a plurality of vectors for the plurality of blocks;
a mapper circuit that is configured to construct a symbol vector based on the plurality of vectors, wherein the plurality of vectors correspond to a plurality of sub-constellations and the symbol vector corresponds to a constellation, and the constellation is a cartesian product of the plurality of sub-constellations, and wherein a product of a vector size of each of the plurality of vectors is equal to a number of channel uses; and
an antenna that is configured to transmit the constructed symbol vector over a radio frequency (RF) signal to a receiving device, wherein the constructed symbol vector represents a symbol modulated in the RF signal.
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