Methods and systems for encoding and decoding based on partitioned complementary sequences

An apparatus comprising:

• an antenna;
• a radio configured to transmit and receive wireless communications via the antenna;
• and
• processing circuity configured to control the radio to establish a wireless communications link with a receiving communications device;
• wherein the processing circuitry is further configured to:
• generate a partitioned complementary sequence based on information bits for transmission, the partitioned complementary sequence comprising zero-valued elements;
• encode a plurality of symbols on a plurality of orthogonal subcarriers using the partitioned complementary sequence, wherein the processing circuitry is configured to map additional information bits for encoding on subcarriers associated with the zero-valued elements of the partitioned complementary sequence;
• and
• control the radio to transmit the plurality of symbols on the plurality of orthogonal subcarriers via the antenna.