Abstract: Embodiments are directed to binary phase shift key modulating a first pilot symbol according to a reference sequence, and differentially binary phase shift key modulating a second pilot symbols. The original reference sequence and the delayed differentially modulated sequence are then combined before performing an Inverse Fast Fourier Transform and inserting a guard interval. Receiver operations are an inverse of the transmitter operations, which were just discussed. The receiver does not have to know the reference sequence. Embodiments are directed to specifying a plurality of seeds that are bit patterns each having r bits not all of which have a value of zero, extending the seeds into respective sequences by applying to each seed a recurrence formula; and using one of the sequences as a comb sequence and using the sequences other than the comb sequence as binary phase shift keying patterns.

Abstract: Embodiments are directed to binary phase shift key modulating a first pilot symbol according to a reference sequence, and differentially binary phase shift key modulating a second pilot symbols. The original reference sequence and the delayed differentially modulated sequence are then combined before performing an Inverse Fast Fourier Transform and inserting a guard interval. Receiver operations are an inverse of the transmitter operations, which were just discussed. The receiver does not have to know the reference sequence. Embodiments are directed to specifying a plurality of seeds that are bit patterns each having r bits not all of which have a value of zero, extending the seeds into respective sequences by applying to each seed a recurrence formula; and using one of the sequences as a comb sequence and using the sequences other than the comb sequence as binary phase shift keying patterns.

Abstract: Embodiments are directed to binary phase shift key modulating a first pilot symbol according to a reference sequence, and differentially binary phase shift key modulating a second pilot symbols. The original reference sequence and the delayed differentially modulated sequence are then combined before performing an Inverse Fast Fourier Transform and inserting a guard interval. Receiver operations are an inverse of the transmitter operations, which were just discussed. The receiver does not have to know the reference sequence. Embodiments are directed to specifying a plurality of seeds that are bit patterns each having r bits not all of which have a value of zero, extending the seeds into respective sequences by applying to each seed a recurrence formula; and using one of the sequences as a comb sequence and using the sequences other than the comb sequence as binary phase shift keying patterns.

Abstract: According to one general aspect, a method including receiving noisy data via a communications channel, wherein the noisy data includes a clean data component and a noise component. In various embodiments, the method may also include decoding, utilizing a low-density lattice code (LDLC) matrix, the received noisy data to substantially recover the clean data component. In some embodiments, the LDLC matrix may not include a matrix of less than a length of six cycles. In one embodiment, the LDLC matrix may be algebraically constructed. In various embodiments, the method may include storing the decoded clean data component.

Abstract: According to one general aspect, a method including receiving noisy data via a communications channel, wherein the noisy data includes a clean data component and a noise component. In various embodiments, the method may also include decoding, utilizing a low-density lattice code (LDLC) matrix, the received noisy data to substantially recover the clean data component. In some embodiments, the LDLC matrix may not include a matrix of less than a length of six cycles. In one embodiment, the LDLC matrix may be algebraically constructed. In various embodiments, the method may include storing the decoded clean data component.

Abstract: Embodiments are directed to binary phase shift key modulating a first pilot symbol according to a reference sequence, and differentially binary phase shift key modulating a second pilot symbols. The original reference sequence and the delayed differentially modulated sequence are then combined before performing an Inverse Fast Fourier Transform and inserting a guard interval. Receiver operations are an inverse of the transmitter operations, which were just discussed. The receiver does not have to know the reference sequence. Embodiments are directed to specifying a plurality of seeds that are bit patterns each having r bits not all of which have a value of zero, extending the seeds into respective sequences by applying to each seed a recurrence formula; and using one of the sequences as a comb sequence and using the sequences other than the comb sequence as binary phase shift keying patterns.