A transmitter encoding apparatus includes a multiplexer and a first transmitter encoder. The multiplexer receives a first digital signal and a second signal and to generate an output, in which the output of the multiplexer includes M-bit code words of the first digital signal and M-bit code words of the second digital signal arranged in an interleaved manner. The first transmitter encoder receives the output of the multiplexer and generates N-bit code words, and N is not equal to M. The first transmitter encoder determines a current N-bit code word of the N-bit code words according to the output of the multiplexer and a disparity of a previous N-bit code word of the N-bit code words. The first transmitter encoder transmits the N-bit code words to a receiver decoding apparatus including a demultiplexer and a first receiver decoder configured to decode the N-bit code words.

Methods, apparatuses and systems directed to complementary sequence (CS) encoding and encoded CS transmissions are provided. Among the apparatuses is apparatus having a transmitter that may be configured to (i) transmit an encoded CS via a block based, e.g., orthogonal frequency division multiplexing (OFDM), waveform, and/or (ii) generate the encoded CS using a plurality of seed sequences and a plurality of information items, wherein: of the elements of the encoded CS encodes a first set of the plurality of information items; (b) phases of the encoded-CS elements encode a second set of the plurality of information items); and (c) the encoded-CS elements define a number of zeros that encode a third set of the plurality of information items. The encoded-CS elements may define respective numbers of zeros that collectively form the number of zeros that encode the third information-item set.

A receiver decoding apparatus includes a first receiver decoder, a demultiplexer, a first receiver encoder and a second receiver decoder. The first receiver decoder decodes a plurality of N-bit code words received from a transmitter encoding apparatus to generate a plurality of I-bit code words, wherein N and I are both positive integers and N is not equal to I. The demultiplexer alternately deinterleaves and assigns the plurality of I-bit code words to a plurality of output terminals of the demultiplexer. The first receiver encoder encodes a plurality of outputs of the output terminals of the demultiplexer to a fifth digital signal comprising a plurality of J-bit code words and a sixth digital signal comprising a plurality of J-bit code words, wherein J is a positive integer and not equal to I. The second receiver decoder decodes the fifth digital signal and the sixth digital signal.

Methods, apparatuses and systems directed to complementary sequence (CS) encoding and encoded CS transmissions are provided. Among the apparatuses is apparatus having a transmitter that may be configured to (i) transmit an encoded CS via a block based, e.g., orthogonal frequency division multiplexing (OFDM), waveform, and/or (ii) generate the encoded CS using a plurality of seed sequences and a plurality of information items, wherein: of the elements of the encoded CS encodes a first set of the plurality of information items; (b) phases of the encoded-CS elements encode a second set of the plurality of information items); and (c) the encoded-CS elements define a number of zeros that encode a third set of the plurality of information items. The encoded-CS elements may define respective numbers of zeros that collectively form the number of zeros that encode the third information-item set.

A receiver decoding apparatus includes a first receiver decoder, a demultiplexer, a first receiver encoder and a second receiver decoder. The first receiver decoder decodes a plurality of N-bit code words received from a transmitter encoding apparatus to generate a plurality of I-bit code words, wherein N and I are both positive integers and N is not equal to I. The demultiplexer alternately deinterleaves and assigns the plurality of I-bit code words to a plurality of output terminals of the demultiplexer. The first receiver encoder encodes a plurality of outputs of the output terminals of the demultiplexer to a fifth digital signal comprising a plurality of J-bit code words and a sixth digital signal comprising a plurality of J-bit code words, wherein J is a positive integer and not equal to I. The second receiver decoder decodes the fifth digital signal and the sixth digital signal.

A transmitter encoding apparatus includes a multiplexer and a first transmitter encoder. The multiplexer receives a first digital signal and a second signal and to generate an output, in which the output of the multiplexer includes M-bit code words of the first digital signal and M-bit code words of the second digital signal arranged in an interleaved manner. The first transmitter encoder receives the output of the multiplexer and generates N-bit code words, and N is not equal to M. The first transmitter encoder determines a current N-bit code word of the N-bit code words according to the output of the multiplexer and a disparity of a previous N-bit code word of the N-bit code words. The first transmitter encoder transmits the N-bit code words to a receiver decoding apparatus including a demultiplexer and a first receiver decoder configured to decode the N-bit code words.

Various embodiments are generally directed to an apparatus, method and other techniques to perform beamforming training in a MIMO environment. Some embodiments may include communicating one or more beamforming refinement packets having training subfields with orthogonal structures such that devices may simultaneously perform beamforming training for each pair of phased array antennas. Embodiments may also include the beamforming refinement packets with channel estimation fields with orthogonal structures.

Various embodiments are generally directed to an apparatus, method and other techniques to perform beamforming training in a MIMO environment. Some embodiments may include communicating one or more beamforming refinement packets having training subfields with orthogonal structures such that devices may simultaneously perform beamforming training for each pair of phased array antennas. Embodiments may also include the beamforming refinement packets with channel estimation fields with orthogonal structures.

Embodiments herein achieve a method and system for selecting non-coherent spreading sequences with binary alphabets {0, 1} with variable spreading factors. The method generates circular shift equivalent sets of spreading sequences by circularly shifting base sequences with elements {1, 0} and having at least one variable spreading factor. The method determines whether each spreading sequence in the circular shift equivalent set meets pre-defined spreading sequence criteria. The spreading sequence criteria comprise balanced criteria, a non- repetition criteria, non-circular criteria, and conjugate criteria. Furthermore, the method selects the spreading sequence from expansions of at least one spreading sequence from the circular shift equivalent sets in response to determining that the spreading sequences in the circular shift equivalent sets meets the pre-defined spreading sequence criteria.

Various embodiments are generally directed to an apparatus, method and other techniques to perform beamforming training in a MIMO environment. Some embodiments may include communicating one or more beamforming refinement packets having training subfields with orthogonal structures such that devices may simultaneously perform beamforming training for each pair of phased array antennas. Embodiments may also include the beamforming refinement packets with channel estimation fields with orthogonal structures.