Data communications and storage systems require error control techniques and digital modulation schemes to be transferred efficiently and successfully. Constellation shaping based on probabilistic amplitude shaping (PAS) offers an energy-efficient transmission in particular for long shaping blocks. However, longer shaping blocks can cause burst errors and enhancement of bit error rates besides longer latency to complete distribution matcher and dematcher operations. Methods and systems are disclosed that provide a way to resolve the issues by introducing a dual concatenation of pre-shaping and post-shaping error correction codes to mitigate burst errors of shaping. This enables low-complexity, high-performance and parallel architecture with a balanced overhead of dual-concatenation codes for shaping systems.

Architectures for inter-converting bitstreams and symbol streams of PAM and/or QAM constellations of different sizes that are not base-2 integers. Some of such constellations may be Gray-coded, and the constellation mapping may be performed to achieve an equiprobable distribution of different constellation symbols. Some embodiments may be compatible with FEC schemes. In an example embodiment, a transmitter DSP may employ a conventional constellation mapper preceded by an electronic encoder programmed to exclude some constellation-symbol labels from the bitstream applied to the mapper. In different embodiments, the electronic encoder may employ a CCDM and/or a long-division operation to select some amplitudes of the constellation and to exclude others. At least some embodiments are beneficially capable of achieving a smaller gap to the Shannon limit than comparable conventional solutions.

Provided are a data modulation method and apparatus, and a storage medium. The method includes: modulating a data sequence [b(i)] to obtain a data sequence [s(k)]; wherein [s(k)] has the following characteristics: in a case where $k=2i,s\left(k\right)=\frac{e^{j\left(\frac{\pi }{2}\left(i\mathrm{mod}2\right)+\theta \right)}}{\sqrt{2}}[\left(1-2b\left(i\right)\right)+j(1-2b$

A method of reducing transmission power for an encoded data stream includes the steps of receiving an incoming data stream having equal probability for a plurality of incoming data bits, assigning a symbol scheme to the received data bits of the incoming data stream according to probabilities of occurrence of individual ones of the received data bits, and transmitting an outgoing data stream according to the assigned symbol scheme having a second average transmit power, different than the first average transmit power, for a plurality of outgoing symbols.

Provided are a data modulation method and device, a data demodulation method and device, a service node, a terminal, and a medium. The data modulation method is applied to the service node, and the data modulation method includes that: a modulation parameter A is determined according to a modulation manner of data; and the data is modulated according to a target constellation point symbol, where the target constellation point symbol is a product of A and X, and X is an initial constellation point symbol corresponding to the modulation manner.

A technique of mapping data, suitable for Peak to Average Power Ratio (PAPR) reduction while transmitting data portions via a communication channel limited by a peak power p.sub.peak. The mapping is performed by utilizing a Markovian symbol transition probability distribution with quantized probabilities and by selecting, for a specific data portion at a current channel state, such a binary symbol (called thinned label) which allows puncturing one or more bits in the thinned label's bit sequence before transmission.

Provided in the embodiments of the present disclosure are a carrier phase tracking method and device for an orthogonal frequency division multiplexing (OFDM) multi-carrier system. The method includes: performing frequency domain tracking on a received current OFDM symbol and determining a phase of each subcarrier; analyzing a phase curve of all subcarriers and determining an inter-symbol phase average offset, and the inter-symbol phase average offset is used to characterize an estimated value of a difference obtained by subtracting a second value from a first value, the first value is a carrier phase value of the current OFDM symbol, and the second value is an estimated value of a carrier phase of a previous OFDM symbol; and performing time domain tracking by using the inter-symbol phase average offset as an input phase and determining an estimated value of a carrier phase of the current OFDM symbol.

Methods, apparatus, and systems for reducing Peak Average Power Ratio (PAPR) in signal transmissions are described. In one example aspect, a wireless communication method includes determining, for an input sequence, an output sequence corresponding to an output of a convolutional modulation between a plurality of values and an intermediate sequence. The intermediate sequence is generated by inserting a set of coefficients between coefficients of the input sequence. Each non-zero coefficient of the set of coefficients is inserted between a first adjacent coefficient and a second adjacent coefficient. Each non-zero coefficient has a power that is between a first power of the first adjacent coefficient and a second power of the second adjacent coefficient and a phase value between a first phase value of the first adjacent coefficient and a second phase value of the second adjacent coefficient. The method also includes generating a waveform using the output sequence.

A transmitting apparatus is disclosed. The transmitting apparatus includes an encoder to perform channel encoding with respect to bits and generate a codeword, an interleaver to interleave the codeword, and a modulator to map the interleaved codeword onto a non-uniform constellation according to a modulation scheme, and the constellation may include constellation points defined based on various tables according to the modulation scheme.

A combined symbol constellation may be selected from a uniform symbol constellation that is supported by a de-mapper to provide additional power split options while reducing modifications to the de-mapper. In some examples, a signal may be constructed according to a combined symbol constellation selected from a larger uniform symbol constellation based on a desired power-ratio. The signal may include a base-layer, used to communicate a first set of data, and an enhancement-layer, used to communicate a second set of data, in accordance with the selected combined symbol constellation. The signal may be received and de-mapped according to the combined symbol constellation at a de-mapper that supports a uniform symbol constellation that is larger than the combined symbol constellation.