# US 11,121,903 B2 · Distribution matching for probabilistic constellation shaping with an arbitrary input/output alphabet

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- Number: US 11,121,903 B2
- Document ID: US11121903B2
- Status: Granted
- Kind: B2
- Application number: 16/152,351
- Filed: 2018-10-04
- Published: 2019-05-16
- Granted: 2021-09-14
- Earliest claimed: 2017-10-04
- Assignees: Infinera Corporation
- Applicants: Infinera Corporation
- Inventors: Mehdi Torbatian; Deyuan Chan; Han Henry Sun; Sandy Thomson; Kuang-Tsan Wu
- Web page: https://patentgrep.com/patent/US11121903B2

## CPC

- H04L 27/362: {Modulation using more than one carrier, e.g. with quadrature carriers, separately amplitude modulated (H04L27/366 takes precedence)}
- H04B 10/0779: {Monitoring line transmitter or line receiver equipment}
- H04B 10/5161: {Combination of different modulation schemes}
- H04B 10/541: {Digital intensity or amplitude modulation}
- H04J 14/0205: {Select and combine arrangements, e.g. with an optical combiner at the output after adding or dropping}
- H04J 14/0226: {Fixed carrier allocation, e.g. according to service}
- H04L 1/0041: {Arrangements at the transmitter end}
- H04L 1/0042: {Encoding specially adapted to other signal generation operation, e.g. in order to reduce transmit distortions, jitter, or to improve signal shape (H04L1/0067 takes precedence)}
- H04L 1/005: {Iterative decoding, including iteration between signal detection and decoding operation}
- H04L 1/0057: {Block codes (H04L1/0061, H04L1/0064 take precedence)}
- H04L 25/067: {providing soft decisions, i.e. decisions together with an estimate of reliability (H04L25/068 and H04L25/069 take precedence; sequence estimation techniques H04L25/03178)}
- H04L 25/49: using code conversion at the transmitter; using predistortion; using insertion of idle bits for obtaining a desired frequency spectrum; using three or more amplitude levels {; Baseband coding techniques specific to data transmission systems (spectral shaping H04L25/03828)}
- H04L 27/3433: {using an underlying square constellation}
- H04L 2025/03611: {Iterative algorithms}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)
- H04B: TRANSMISSION
- H04J: MULTIPLEX COMMUNICATION (transmission in general H04B; peculiar to transmission of digital information H04L5/00; systems for the simultaneous or sequential transmission of more than one television signal H04N7/08; in exchanges H04Q11/00; stereophonic systems H04S)

## Abstract

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.

## Claims

### Claim 1

An apparatus, comprising:
a local oscillator laser that supplies local oscillator light;
an optical hybrid circuit that receives an incoming optical signal and the local oscillator light, the incoming optical signal being modulated in accordance with an m-quadrature modulated optical signal, where m is greater than or equal to 16;
a photodetector circuit that receives an optical output from the optical hybrid circuit and generates electrical signals;
a decoder circuit that receives a codeword based on the electrical signals, the codeword includes n codeword symbols, where n is an integer, the codeword being indicative of a distribution of modulation symbols carried by the incoming optical signal such that first ones of the modulation symbols having an associated first amplitude are transmitted more frequently than second ones of the modulation symbols having an associated second amplitude that is different than the first amplitude; and
a clock circuit that generates a clock signal,
wherein the decoder circuit processes each of the modulation symbols during a corresponding one of a plurality of clock cycles of the clock signal, such that, during n clock cycles of the plurality of clock cycles of the clock signal, the decoder circuit outputs a data sequence based on the code word and fixed point representations of the codeword, where k is an integer.

### Claim 2 (depends on 1)

An apparatus in accordance with claim 1, wherein third ones of the modulation symbols having an associated third amplitude are transmitted less frequently than the first and second ones of the modulation symbols.

### Claim 3 (depends on 2)

An apparatus in accordance with claim 2, wherein fourth ones of the modulation symbols having an associated fourth amplitude are transmitted less frequently than the first, second, and third ones of the modulation symbols.

### Claim 4

An apparatus, comprising:
a local oscillator laser that supplies local oscillator light;
an optical hybrid circuit that receives an incoming optical signal and the local oscillator light, the incoming optical signal being modulated in accordance with an m-quadrature modulated optical signal, where m is greater than or equal to 16;
a photodetector circuit that receives an optical output from the optical hybrid circuit and generates electrical signals;
a decoder circuit that receives a codeword based on the electrical signals, the codeword includes n codeword symbols, where n is an integer, the codeword being indicative of a distribution of modulation symbols carried by the incoming optical signal such that first ones of the modulation symbols having an associated first amplitude are transmitted more frequently than second ones of the modulation symbols having an associated second amplitude that is different than the first amplitude; and
a clock circuit that generates a clock signal,
wherein the decoder circuit outputs, during n clock cycles of the clock signal and based on fixed point representations of the codeword, a data sequence based on the codeword, the data sequence having k bits, where k is an integers; and
an inverse labelling circuit converting each of a plurality of binary or non-binary symbols to a corresponding one of the n codeword symbols.

### Claim 5 (depends on 4)

An apparatus in accordance with claim 4, further including a forward error correcting (FEC) decoding circuit that decodes in-phase and quadrature symbols, in accordance with a forward error correction code, to provide the plurality of binary or non-binary symbols.

### Claim 6 (depends on 5)

An apparatus in accordance with claim 5, wherein the binary or non-binary symbols do not include parity bits.

### Claim 7 (depends on 5)

An apparatus in accordance with claim 5, further including a multiplexer that multiplexes the in-phase and quadrature symbols and supplies the multiplexed in-phase and quadrature symbols to the FEC decoding circuit.

### Claim 8

An apparatus comprising:
a local oscillator laser that supplies local oscillator light;
an optical hybrid circuit that receives an incoming optical signal and the local oscillator light, the incoming optical signal being modulated in accordance with an m-quadrature modulated optical signal, where m is greater than or equal to 16;
a photodetector circuit that receives an optical output from the optical hybrid circuit and generates electrical signals;
a decoder circuit that receives a codeword based on the electrical signals, the codeword includes n codeword symbols, where n is an integer, the codeword being indicative of a distribution of modulation symbols carried by the incoming optical signal such that first ones of the modulation symbols having an associated first amplitude are transmitted more frequently than second ones of the modulation symbols having an associated second amplitude that is different than the first amplitude; and
a clock circuit that generates a clock signal,
wherein the decoder circuit outputs, during n clock cycles of the clock signal and based on fixed point representations of the codeword, a data sequence based on the codeword, the data sequence having k bits, where k is an integers, and,
wherein the decoder circuit calculates a parameter, x, based on one of the n codeword symbols, calculates a parameter, y, such that y is greater than n, and determines that x is within a sub-interval of y corresponding to said one of the n codeword symbols.

### Claim 9 (depends on 8)

An apparatus in accordance with claim 8, wherein the encoder circuit determines y, such that y further satisfies:
2w≤y≤2w+1
where w is a lowest integer, such that y is greater than n.

### Claim 10 (depends on 8)

An apparatus in accordance with claim 8, wherein the decoder circuit multiplies parameter x by a scaling factor and multiplies y by the scaling factor.

### Claim 11 (depends on 8)

An apparatus in accordance with claim 8, wherein said one of the n codeword symbols is a first one of the n codeword symbols, the encoder circuit redefining the sub-interval based on a number remaining codeword symbols after the first one of the n codeword symbols is output.

### Claim 12 (depends on 11)

An apparatus in accordance with claim 11, wherein first ones of the remaining codeword symbols have a first value and second ones of the remaining codeword symbols have a second value.

### Claim 13 (depends on 11)

An apparatus in accordance with claim 11, wherein each of the remaining codewords symbols has a respective one of a plurality of values, a number of the plurality of values being greater than two.

### Claim 14 (depends on 8)

An apparatus in accordance with claim 8, further including a memory that stores selected ones of the k bits of the data sequence prior to outputting the data sequence.

### Claim 15 (depends on 14)

An apparatus in accordance with claim 14, wherein the memory is a buffer.

### Claim 16

An apparatus, comprising:
a local oscillator laser that supplies local oscillator light;
an optical hybrid circuit that receives an incoming optical signal and the local oscillator light, the incoming optical signal being modulated in accordance with an m-quadrature modulated optical signal, where m is greater than or equal to 16;
a photodetector circuit that receives an optical output from the optical hybrid circuit and generates electrical signals;
a decoder circuit that receives a codeword based on the electrical signals, the codeword includes n codeword symbols, where n is an integer, the codeword being indicative of a distribution of modulation symbols carried by the incoming optical signal such that first ones of the modulation symbols having an associated first amplitude are transmitted more frequently than second ones of the modulation symbols having an associated second amplitude that is different than the first amplitude; and
a clock circuit that generates a clock signal,
wherein the decoder circuit outputs, during n clock cycles of the clock signal and based on fixed point representations of the codeword, a data sequence based on the codeword, the data sequence having k bits, where k is an integers,
wherein the first amplitude is less than the second amplitude.

### Claim 17

An apparatus, comprising:
a decoder circuit including:
an input that receives a codeword, the codeword includes n codeword symbols, where n is an integer, the codeword being indicative of a distribution of modulation symbols carried by an optical signal modulated in accordance with an m-quadrature modulated optical signal (QAM) where m is greater than or equal to 16, first ones of the modulation symbols having an associated first amplitude are transmitted more frequently than second ones of the modulation symbols having an associated second amplitude that is different than the first amplitude; and
a clock circuit that generates a clock signal,
wherein the decoder circuit processes each of the modulation symbols during a corresponding one of a plurality of clock cycles of the clock signal, such that, during n clock cycles of the plurality of clock cycles of the clock signal, the decoder circuit outputs a data sequence having k bits based on the codeword and fixed point representations of the codeword, where k is an integer.

### Claim 18 (depends on 17)

An apparatus in accordance with claim 17, further including:
a local oscillator laser that supplies local oscillator light;
an optical hybrid circuit that receives the optical signal and the local oscillator light;
a photodetector circuit that receives an optical output from the optical hybrid circuit and generates electrical signals, the decoder circuit that receives the codeword based on the electrical signals.

### Claim 19 (depends on 17)

An apparatus in accordance with claim 17, wherein third ones of the modulation symbols having an associated third amplitude are transmitted less frequently than the first and second ones of the modulation symbols.

### Claim 20 (depends on 19)

An apparatus in accordance with claim 19, wherein fourth ones of the modulation symbols having an associated fourth amplitude are transmitted less frequently than the first, second, and third ones of the modulation symbols.

### Claim 21 (depends on 17)

An apparatus in accordance with claim 17, further including a memory that stores selected ones of the k bits of the data sequence in a buffer prior to outputting the data sequence.

### Claim 22 (depends on 21)

An apparatus in accordance with claim 21, wherein the memory is a buffer.

### Claim 23

An apparatus, comprising:
a decoder circuit including:
an input that receives a codeword, the codeword includes n codeword symbols, where n is an integer, the codeword being indicative of a distribution of modulation symbols carried by an optical signal modulated in accordance with an m-quadrature modulated optical signal (QAM) where m is greater than or equal to 16, first ones of the modulation symbols having an associated first amplitude are transmitted more frequently than second ones of the modulation symbols having an associated second amplitude that is different than the first amplitude; and
a clock circuit that generates a clock signal,
wherein, based on fixed point representations of the codeword, the decoder circuit outputs, during n clock cycles of the clock signal, a data sequence based on the codeword, the data sequence having k bits, where k is an integer; and
an inverse labelling circuit converting each of a plurality of binary or non-binary symbols to a corresponding one of the n codeword symbols.

### Claim 24 (depends on 23)

An apparatus in accordance with claim 23, further including a forward error correcting (FEC) decoding circuit that decodes in-phase and quadrature symbols, in accordance with a forward error correction code, to provide the plurality of binary or non-binary symbols.

### Claim 25 (depends on 24)

An apparatus in accordance with claim 24, wherein the binary or non-binary symbols do not include parity bits.

### Claim 26 (depends on 24)

An apparatus in accordance with claim 24, further including a multiplexer that multiplexes the in-phase and quadrature symbols and supplies the multiplexed in-phase and quadrature symbols to the FEC decoding circuit.

### Claim 27

An apparatus, comprising:
a decoder circuit including:
an input that receives a codeword, the codeword includes n codeword symbols, where n is an integer, the codeword being indicative of a distribution of modulation symbols carried by an optical signal modulated in accordance with an m-quadrature modulated optical signal (QAM) where m is greater than or equal to 16, first ones of the modulation symbols having an associated first amplitude are transmitted more frequently than second ones of the modulation symbols having an associated second amplitude that is different than the first amplitude; and
a clock circuit that generates a clock signal,
wherein, based on fixed point representations of the codeword, the decoder circuit outputs, during n clock cycles of the clock signal, a data sequence based on the codeword, the data sequence having k bits, where k is an integer,
wherein the decoder circuit calculates a parameter, x, based on one of the n codeword symbols, calculates a parameter, y, such that y is greater than n, and determines that x is within a sub-interval of y corresponding to said one of the n codeword symbols.

### Claim 28 (depends on 27)

An apparatus in accordance with claim 27, wherein the encoder circuit determines y, such that y further satisfies:
2w≤y≤2w+1
where w is a lowest integer, such that y is greater than n.

### Claim 29 (depends on 27)

An apparatus in accordance with claim 27, wherein the decoder circuit multiplies parameter x by a scaling factor and multiplies y by the scaling factor.

### Claim 30 (depends on 27)

An apparatus in accordance with claim 27, wherein said one of the n codeword symbols is a first one of the n codeword symbols, the encoder circuit redefining the sub-interval based on a number remaining codeword symbols after the first one of the n codeword symbols is output.

### Claim 31 (depends on 30)

An apparatus in accordance with claim 30, wherein first ones of the remaining codeword symbols have a first value and second ones of the remaining codeword symbols have a second value.

### Claim 32 (depends on 30)

An apparatus in accordance with claim 30, wherein each of the remaining codewords symbols has a respective one of a plurality of values, a number of the plurality of values being greater than two.

### Claim 33

An apparatus, comprising:
a decoder circuit including:
an input that receives a codeword, the codeword includes n codeword symbols, where n is an integer, the codeword being indicative of a distribution of modulation symbols carried by an optical signal modulated in accordance with an m-quadrature modulated optical signal (QAM) where m is greater than or equal to 16, first ones of the modulation symbols having an associated first amplitude are transmitted more frequently than second ones of the modulation symbols having an associated second amplitude that is different than the first amplitude; and
a clock circuit that generates a clock signal,
wherein, based on fixed point representations of the codeword, the decoder circuit outputs, during n clock cycles of the clock signal, a data sequence based on the codeword, the data sequence having k bits, where k is an integer,
wherein the first amplitude is less than the second amplitude.