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.

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.

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.

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.

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.

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.

A method of spatially multiplexing data comprising a signal vector, the method comprising selecting first and second modulation schemes for the data transmission wherein the second modulation scheme is an interpolation in the plane of the first modulation scheme; and further wherein the modulation schemes are selected so as to maintain the same minimum Euclidean distance between vectors comprising the first and second modulation schemes as the minimum Euclidean distance within the first and second modulation schemes; and selecting a plurality of antennae, each of the plurality to concurrently transmit respective symbols of the signal vector.

A telecommunication method which includes mapping, by a mapper, input data to points of a constellation, modulating, by a modulator, points of the constellation to generate modulated symbols, and transmitting a radio signal representative of the modulated symbols. The constellation includes a set of N points, the coordinates of which expressed in polar form ?.sub.n?e.sup.j?n, n=1, . . . , N, referred to as polar coordinates, are determined such that a.sub.n+1=a.sub.n+p, p>0, the real number being the pitch amplitude of the constellation.

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.