A transmission device that improves data reception quality includes: a weighting synthesizer that generates a first precoded signal and a second precoded signal from a first baseband signal and a second baseband signal, respectively; a phase changer that applies a phase change of i×Δλ to the second precoded signal; an inserter that inserts a pilot signal into the second precoded signal applied with the phase change; and a phase changer that applies a phase change to the second precoded signal applied with the phase change and inserted with the pilot signal. Δλ satisfies π/2 radians<Δλ<π radians or π radians<Δλ<3π/2 radians. Each of the first baseband signal and the second baseband signal is modulated via a modulation scheme of quadrature amplitude modulation (QAM) using non-uniform mapping.

Pulse amplitude modulation (PAM) encoding for a communication bus is disclosed. In particular, various two-wire communication buses may encode bits using three-level PAM (PAM-3) or five-level PAM (PAM-5) to increase bit transmission without requiring increases to clock frequencies or adding additional pins. Avoiding increases in clock frequencies helps reduce the risk of electromagnetic interference (EMI), and avoiding use of extra pins avoids cost increases for integrated circuits (ICs).

A transmission device that improves data reception quality includes: a weighting synthesizer that generates a first precoded signal and a second precoded signal from a first baseband signal and a second baseband signal, respectively; a phase changer that applies a phase change of i×Δλ to the second precoded signal; an inserter that inserts a pilot signal into the second precoded signal applied with the phase change; and a phase changer that applies a phase change to the second precoded signal applied with the phase change and inserted with the pilot signal. Δλ satisfies π/2 radians<Δλ<π radians or π radians<Δλ<3π/2 radians. Each of the first baseband signal and the second baseband signal is modulated via a modulation scheme of quadrature amplitude modulation (QAM) using non-uniform mapping.

Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.

Systems, methods and devices for communicating comprise one or more of a computer-readable media, a computer, a satellite communication device and a mobile device, wherein the at least one of a computer-readable media, a computer, a satellite communication device and a mobile device to perform at least one of supplying data as input communication symbols to an encoder, which converts the input communication symbols into transmittable waveforms having a head function and a tail function, which are different. A transmitter transmits transmittable waveforms over a communication channel, which is received by a receiver, then demodulated and output communication symbols carrying the data to at least one of a user, a secondary computer-readable media, a secondary computer, a secondary satellite communication device and a secondary mobile device.

Disclosed herein is a method for transmitting digital data in a super channel, in which a set of carriers are packed in a predetermined bandwidth. The set of carriers comprises higher and lower edge carriers having the highest and lowest wavelengths, respectively, among said set of earners, wherein data is transmitted via the higher and lower edge carriers using a corresponding modulation format, each modulation format using a constellation diagram comprising a number of symbols, wherein a binary address is associated with each symbol. Said method comprises the steps of: separating digital data to be transmitted via each of said higher and lower edge carriers into corresponding first and second data streams, and for each of said higher and lower edge carriers, mapping the data of the first data stream to predetermined first bit positions within the binary symbol addresses and the data of the second data stream to predetermined second bit positions within the binary symbol addresses, wherein said first bit positions are bit positions which have an error probability less than the average error probability of all bit positions.

A transmission device that improves data reception quality includes: a weighting synthesizer that generates a first precoded signal and a second precoded signal from a first baseband signal and a second baseband signal, respectively; a phase changer that applies a phase change of i to the second precoded signal; an inserter that inserts a pilot signal into the second precoded signal applied with the phase change; and a phase changer that applies a phase change to the second precoded signal applied with the phase change and inserted with the pilot signal. satisfies /2 radians<< radians or radians<<3/2 radians. Each of the first baseband signal and the second baseband signal is modulated via a modulation scheme of quadrature amplitude modulation (QAM) using non-uniform mapping.

Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.

A transmission device that improves data reception quality includes: a weighting synthesizer that generates a first precoded signal and a second precoded signal from a first baseband signal and a second baseband signal, respectively; a phase changer that applies a phase change of i to the second precoded signal; an inserter that inserts a pilot signal into the second precoded signal applied with the phase change; and a phase changer that applies a phase change to the second precoded signal applied with the phase change and inserted with the pilot signal. satisfies /2 radians<< radians or radians<<3/2 radians. Each of the first baseband signal and the second baseband signal is modulated via a modulation scheme of quadrature amplitude modulation (QAM) using non-uniform mapping.

Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission. In various embodiments, transmitter and receivers utilizing symbol waveforms based on a PSW alphabet designed may be in wireless and/or wired data transmission systems that may or may not include transmitters and receivers employing traditional modulation formats.