Transmitting device, receiving device, and methods for random-access communication

A receiving device for a random-access communication, comprising:

• at least one antenna configured to receive a plurality of radio frequency signals concurrently from a plurality of transmitting devices:
• an equalizer circuit that is configured to estimate a plurality of symbol vectors from the received plurality of radio frequency signals in digital domain, and segregate the plurality of symbol vectors;
• and
• a plurality of decoders, wherein each of the plurality of decoders is configured to decode one segregated symbol vector of the estimated plurality of symbol vectors to obtain a plurality of decoded messages, wherein each decoded message has a sequence of bits that corresponds to data associated with a corresponding transmitting device of the plurality of transmitting devices, wherein the symbol vector is constructed from a plurality of sub-vectors, the plurality of sub-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 sub-vectors is equal to a number of channel uses.

A method for a random-access communication, comprising:

• acquiring, by an encoder of a transmitting device, an input message having a sequence of bits;
• forming, by the encoder of the transmitting device, a plurality of blocks from the sequence of bits;
• and
• determining, by the encoder of the transmitting device, a plurality of vectors for the plurality of blocks;
• constructing, by the transmitting device, 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
• transmitting, by the transmitting device, 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.

A method for a random-access communication, comprising:

• receiving, by a receiving device, a plurality of radio frequency signals concurrently from a plurality of transmitting devices;
• estimating, by the receiving device, a plurality of symbol vectors from the received plurality of radio frequency signals in digital domain, and segregate the plurality of symbol vectors;
• and
• decoding, by the receiving device, each segregated symbol vector of the estimated plurality of symbol vectors to obtain a plurality of decoded messages, wherein each decoded message has a sequence of bits that corresponds to data associated with a corresponding transmitting device of the plurality of transmitting devices, wherein the symbol vector is constructed from a plurality of sub-vectors, the plurality of sub-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 sub-vectors is equal to a number of channel uses.