Systems and methods for communicating using random codewords located within a restricted subset of a multi-dimensional sphere

A transmitter system, comprising:

• a receiver configured to receive a start of epoch message;
• an encoder configured to:
• encode message data as symbols using a rateless code comprising a set of codewords characterized in that they are located within a restricted subset of a multi-dimensional sphere;
• and
• a modulator configured to transmit the symbols encoded by the encoder;
• wherein the receiver is further configured to receive an end of epoch message at one of a predetermined set of times;
• and
• wherein the modulator is configured to transmit the symbols encoded by the encoder until an end of epoch message is received by the receiver.

A receiver system, comprising:

• a decoder configured to select at least one codebook;
• a transmitter configured to transmit at least one start of epoch message;
• a receiver configured to receive observed symbols;
• wherein the decoder is further configured to:
• determine whether a decoding rule is satisfied at each of a predetermined set of decode times;
• and
• when the decoding rule is satisfied:
• decode at least one message based upon the received observed symbols based upon a rateless code comprising a set of codewords characterized in that they are located within a restricted subset of a multi-dimensional sphere;
• and
• cause the transmitter to transmit an end of epoch message.