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An optical transport system is configured to use a modulation scheme in which a phase rotation applied to a sequence of PSK or QAM constellation symbols encoding a codeword of an FEC code produces a modified sequence of PSK or QAM constellation symbols encoding a bit-word that is not a valid codewor

An optical transport system is configured to use a modulation scheme in which a phase rotation applied to a sequence of PSK or QAM constellation symbols encoding a codeword of an FEC code produces a modified sequence of PSK or QAM constellation symbols encoding a bit-word that is not a valid codeword of that FEC code. Based on this property of the modulation scheme, an optical receiver may be configured to relatively accurately recover the absolute phase of the optical carrier wave of the received modulated optical signal by applying maximum likelihood sequence estimation processing to each portion of the signal carrying a valid codeword of the FEC code. For example, for a modulation scheme employing a 2n-PSK constellation, the optical receiver may be able to recover the absolute phase of the optical carrier wave with an accuracy that is better than 360/2n degrees.

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1. An apparatus comprising an optical receiver that comprises: a front-end circuit configured to convert a portion of a modulated optical signal corresponding to a first codeword of a forward error correction (FEC) code into a first set of digital values; anda digital circuit configured to apply max

1. An apparatus comprising an optical receiver that comprises: a front-end circuit configured to convert a portion of a modulated optical signal corresponding to a first codeword of a forward error correction (FEC) code into a first set of digital values; anda digital circuit configured to apply maximum likelihood sequence estimation (MLSE) processing to the first set of digital values, wherein the digital circuit comprises a plurality of parallel processing branches, each configured to: receive a copy of the first set of digital values;apply a respective phase rotation to said copy to generate a respective string of values; andgenerate, based on the respective string of values, a respective measure of a phase of an optical carrier wave of the modulated optical signal; andwherein the digital circuit is configured to recover the first codeword based on the plurality of said measures of the phase generated by said plurality of parallel processing branches. 2. The apparatus of claim 1, wherein the modulated optical signal is modulated using a QAM constellation. 3. The apparatus of claim 1, wherein: the modulated optical signal is modulated using a 2n-PSK constellation, where n is a positive integer; andthe plurality of parallel processing branches includes 2n processing branches. 4. The apparatus of claim 3, wherein n=2. 5. The apparatus of claim 3, wherein: the respective phase rotation is by an angle selected from an angle set consisting of the following angles: 360m/2n degrees, where m=0, 1, 2, . . . , 2n−1; anddifferent processing branches are configured to use different respective angles from said angle set. 6. The apparatus of claim 3, wherein the first codeword has a length of at least 2n bits. 7. The apparatus of claim 3, wherein at least some of the 2n processing branches include respective complex-number multipliers, each configured to apply the respective phase rotation by multiplying each of a plurality of complex numbers generated from the first set of digital values by a complex exponential factor having an argument that is proportional to an angle of the respective phase rotation. 8. The apparatus of claim 1, wherein the FEC code has a rate of ½ or lower. 9. The apparatus of claim 1, wherein: the front-end circuit is configured to mix the modulated optical signal with an optical local-oscillator signal; andthe respective measure of the phase is a measure of a phase mismatch between the optical carrier wave of the modulated optical signal and the optical local-oscillator signal. 10. The apparatus of claim 1, wherein each of the processing branches is further configured to identify a respective candidate codeword based on a plurality of distance measures, each being a measure of a distance between the respective string of values and a respective one of a plurality of codewords of the FEC code. 11. The apparatus of claim 10, wherein the measure of the distance between the respective string of values and the respective one of the plurality of codewords of the FEC code is a squared Euclidean distance. 12. The apparatus of claim 10, wherein the digital circuit further comprises: a selector controller configured to identify a processing branch having a smallest measure in the plurality of the measures of the phase; anda selector configured to recover the first codeword by selecting the respective candidate codeword identified by the processing branch having said smallest measure. 13. The apparatus of claim 10, wherein each of the parallel processing branches comprises: a respective maximum-likelihood detector configured to identify the respective candidate codeword based on the plurality of the distance measures by selecting a codeword, in the plurality of codewords of the FEC code, corresponding to a smallest of the plurality of the distance measures; anda respective sliding-window adder configured to generate the respective measure of the phase by summing 2L+1 of the smallest distance measures, where L is a positive integer, wherein: one of said 2L+1 smallest distance measures corresponds to the first set of digital values;a first L of said 2L+1 smallest distance measures correspond to L sets of digital values generated by the front-end circuit based on a portion of the modulated optical signal corresponding to L codewords that precede the first codeword; anda second L of said 2L+1 smallest distance measures correspond to L sets of digital values generated by the front-end circuit based on a portion of the modulated optical signal corresponding to L codewords that follow the first codeword. 14. The apparatus of claim 13, wherein each of the parallel processing branches further comprises a respective delay line configured to hold the respective candidate codeword for a period of time that enables the respective sliding-window adder to receive the second L of said 2L+1 smallest distance measures from the respective maximum-likelihood detector. 15. The apparatus of claim 1, further comprising an optical transmitter configured to generate the first codeword by including therein a set of information bits and further including therein a set of parity bits corresponding to the set of information bits. 16. The apparatus of claim 15, wherein the optical transmitter is further configured to cause the optical receiver to receive the modulated optical signal by modulating the optical carrier wave with a sequence of constellation symbols that encode the first codeword. 17. The apparatus of claim 16, wherein the optical transmitter is configured to generate said sequence of constellation symbols in a manner that causes a phase-rotated version of said sequence to encode a bit word that is not a codeword of the FEC code.