Provided is a transmission method that improves data reception quality in radio transmission using a single-carrier scheme and/or a multi-carrier scheme. The transmission method includes: generating a plurality of first modulated signals and a plurality of second modulated signals from transmission data, the plurality of first modulated signals being signals generated using a 16 QAM modulation scheme, and the plurality of second modulated signals being signals generated using uniform constellation 64 QAM modulation; generating, from the plurality of first modulated signals and the plurality of second modulated signals, a plurality of first signal-processed signals and a plurality of second signal-processed signals which satisfy a predetermined equation; and changing the predetermined equation when a 64 QAM modulation used to generate the plurality of second modulated signals is switched from the uniform constellation 64 QAM modulation to a non-uniform constellation 64 QAM modulation.

Certain aspects of the disclosure are directed to a method for communicating data from a transmitting circuit to a receiving circuit over a noisy channel. The method can be performed by logic circuitry, and can include encoding data, for transmission over the noisy channel. The data can be encoded, as a shaped-coded modulation signal by shaping the signal based on an amplitude selection algorithm that leads to a symmetrical input and by constructing a trellis having a bounded-energy sequence of amplitude values selected by computing and storing a plurality of channel-related energy constraints based on use of a nonlinear-estimation process, and therein providing an index for the bounded-energy sequence of amplitudes. The method can also include receiving over the noisy channel, the shaped-coded modulation signal, and decoding the data from the shaped-coded modulation signal by using the index to reconstruct the bounded-energy sequence of amplitudes.

Certain aspects of the disclosure are directed to a method for communicating data from a transmitting circuit to a receiving circuit over a noisy channel. The method can be performed by logic circuitry, and can include encoding data, for transmission over the noisy channel. The data can be encoded, as a shaped-coded modulation signal by shaping the signal based on an amplitude selection algorithm that leads to a symmetrical input and by constructing a trellis having a bounded-energy sequence of amplitude values selected by computing and storing a plurality of channel-related energy constraints based on use of a nonlinear-estimation process, and therein providing an index for the bounded-energy sequence of amplitudes. The method can also include receiving over the noisy channel, the shaped-coded modulation signal, and decoding the data from the shaped-coded modulation signal by using the index to reconstruct the bounded-energy sequence of amplitudes.

Consistent with the present disclosure, an encoder circuit is provided at a transmit side of an optical fiber link that maps an input sequence of bits of fixed length k a sequence of symbols of a codeword of length n, such that the symbols of the codeword define a predetermined transmission probability distribution. Preferably, each symbol of the codeword is generated during a corresponding clock cycle, such that after n clock cycles, a complete codeword corresponding to the input bit sequence is output. On a receive end of the link, a decoder is provided that outputs the k-bit sequence every n clock cycles. Accordingly, buffers need not be provided at the output of the encoder and the input of the decoder, such that processing of the input sequence, codewords, and output sequence may be achieved efficiently without large buffers and complicated circuitry. Moreover, the input sequence, with any binary alphabet may be matched to a desired output distribution with any arbitrary alphabet. Accordingly, probabilistic constellation shaping may be achieved over constellations of arbitrary size. In addition, relatively long codewords, may be encoded and decoded with the apparatus and method disclosed herein. Accordingly, for a fixed SNR a higher SE (more bits per symbol) can be achieved. Alternatively, for a fixed SE, a lower SNR may be sufficient. Moreover, the resulting SE may be finely tailored to a particular optical link SNR to provide data transmission rates that are higher than the low order modulation formats that would otherwise be employed for optical signals carried by such links.

Methods (C) for converting a data signal (U). The methods may comprise (i) providing an input symbol stream (IB) of input symbols (Bj), the input symbol stream (IB) being representative for the data signal (U) to be converted and (ii) applying to consecutive disjunct partial input symbol sequences (IB.sup.p) of a number of p consecutive input symbols (IBj) covering said input symbol stream (IB), a distribution matching process (DM) to generate and output a final output symbol stream (OB) or a preform thereof, wherein the distribution matching process (DM) may be formed by a preceding shell mapping process (SM) and a succeeding amplitude mapping process (AM), wherein said shell mapping process (SM) may be configured to form and output to said amplitude mapping process (AM) for each of said consecutive partial input symbol sequences (IB.sup.p) a sequence (s.sup.q) of a number of q shell indices (s), and wherein said amplitude mapping process (AM) may be configured to assign to each shell index (s) a tuple of amplitude values.

Provided is a transmission method that improves data reception quality in radio transmission using a single-carrier scheme and/or a multi-carrier scheme. The transmission method includes: generating a plurality of first modulated signals and a plurality of second modulated signals from transmission data, the plurality of first modulated signals being signals generated using a 16 QAM modulation scheme, and the plurality of second modulated signals being signals generated using uniform constellation 64 QAM modulation; generating, from the plurality of first modulated signals and the plurality of second modulated signals, a plurality of first signal-processed signals and a plurality of second signal-processed signals which satisfy a predetermined equation; and changing the predetermined equation when a 64 QAM modulation used to generate the plurality of second modulated signals is switched from the uniform constellation 64 QAM modulation to a non-uniform constellation 64 QAM modulation.

An optical receiver apparatus includes a photo detector that detects amplitude modified optical signals transmitted through an optical transmission channel and mapped to constellation points and converts the optical signal into electrical signals, a sampling circuit that samples the electrical signals and generates digital signals, and a signal processing circuit that has a two-step equalization algorithm converging actual constellation points into desired constellation points. The two-step equalization algorithm includes a first equalization algorithm that uses multiple modulus in performing an error signal calculation, and a second equalization algorithm that includes a filtering procedure that compares actual constellation points with desired constellation points and an adjustment procedure that iteratively adjusts parameters of the filtering procedure in accordance with the comparison result.

The proposed solution relates to a method and an apparatus in a communication system. The solution includes receiving as an input a frame including of a set of data symbols and reference symbols, each data symbol forming a rectangular symbol constellation of samples, derotating the first symbol of the set on the basis of the reference symbols, and setting phase rotating angle of the first symbol as zero. The solution further includes for each following successive symbol in the set of symbols: performing equalization; reducing the number of samples in the constellation by selecting samples in two or more corners of the constellation by utilizing two or more threshold values; estimating the phase rotating angle of the symbol from the reduced number of samples and derotating the symbol on the basis of the determined phase rotating angle.

A simple construction for a family of non-uniform APSK constellations by the radial isomorphism between squares to circles is provided. The mutual information values indicate gains of at least 0.5 dB up to 1.5 dB with respect to the state of the art, such as the DVB-S2X constellations with 256 symbols. The invention also provides for a low-complexity detector of high-order modulated signals.

A method for encoding K bits of data, wherein K is a multiple of N is provided. The method includes a first step of mapping N consecutive bits of the K bits of data, starting from either its least significant bit or its most significant bit, to a point within a quadrant out of 2.sup.N quadrants of an N-dimensional space. The method includes a second step of mapping the subsequent contiguous N consecutive bits of the K bits of data, to a point within a sub-quadrant out of 2.sup.N quadrants of the N dimensional space within the previous quadrant. The method includes repeating the second step until all K bits of data have been mapped. The method includes a third step of obtaining N coordinate values of N consecutive bits of the data mapped last, wherein the N coordinate values represent the encoded code word for the K bits of data.