Abstract: A method and apparatus for reducing nonlinear phase noise that is induced in an optical transmission system by the interaction of optical amplifier noise and Kerr effect. The apparatus includes an intensity-scaled nonlinear phase noise compensator. The phase noise compensator reduces the nonlinear phase noise by applying a scaled differential signal strength estimate to estimated differential quadrature components or an estimated differential phase for providing a phase noise compensated representation.

Abstract: A method and apparatus for reducing nonlinear phase noise that is induced in an optical transmission system by the interaction of optical amplifier noise and Kerr effect. The apparatus includes an intensity-scaled non-linear phase noise compensator. The phase noise compensator provides a phase noise compensated representation of a differential frequency by combining a measured differential frequency with a scaled differential signal strength estimate. The scale factor is derived from the number of spans in the transmission system.

Abstract: A method and apparatus for reducing nonlinear phase noise that is induced in an optical transmission system by the interaction of optical amplifier noise and Kerr effect. The apparatus includes an intensity-scaled nonlinear phase noise compensator. The phase noise compensator reduces the nonlinear phase noise by rotating a phase estimate by a scaled signal strength estimate for the optical signal or by comparing a complex estimate of the optical signal to curved regions having scaled nonlinear decision boundaries. The scale factor is derived from the number of spans in the transmission system.

Abstract: A method and apparatus for reducing nonlinear phase noise that is induced in an optical transmission system by the interaction of optical amplifier noise and Kerr effect. The apparatus includes an intensity-scaled nonlinear phase noise compensator. The phase noise compensator reduces the nonlinear phase noise by rotating a phase estimate by a scaled signal strength estimate for the optical signal or by comparing a complex estimate to curved regions having scaled nonlinear decision boundaries. The scale factor is derived from the number of spans in the transmission system. Another embodiment of the phase noise compensator uses the scaled signal strength for re-modulating an optical signal.

Abstract: A method and apparatus for reducing nonlinear phase noise that is induced in an optical transmission system by the interaction of optical amplifier noise and Kerr effect. The apparatus includes an intensity-scaled nonlinear phase noise compensator. The phase noise compensator reduces the nonlinear phase noise by rotating a phase estimate by a scaled signal strength estimate for the optical signal or by comparing a complex estimate to curved regions having scaled nonlinear decision boundaries. The scale factor is derived from the number of spans in the transmission system. Another embodiment of the phase noise compensator uses the scaled signal strength for re-modulating an optical signal.

Abstract: Methods and apparatus are described to transmit and receive information encoded in multilevel optical signals that take on at least three intensity levels. Intensity levels of a transmitted multilevel optical signal are optimized to minimize a transmitted optical power required to achieve a specified decision error probability, taking account of an arbitrary admixture of impairments, including signal-dependent noise, signal-independent noise, a finite transmitter extinction ratio, and intersymbol interference. The optimizations described are implemented using analytical or numerical techniques, depending on the admixture of impairments, and can be used to achieve equal or unequal decision error probabilities at a set of decision thresholds.

Abstract: Methods and apparatus are described to transmit and receive information encoded in multilevel optical signals that take on at least three intensity levels. Intensity levels of a transmitted multilevel optical signal are optimized to minimize a transmitted optical power required to achieve a specified decision error probability, taking account of an arbitrary admixture of impairments, including signal-dependent noise, signal-independent noise, a finite transmitter extinction ratio, and intersymbol interference. The optimizations described are implemented using analytical or numerical techniques, depending on the admixture of impairments, and can be used to achieve equal or unequal decision error probabilities at a set of decision thresholds.

Abstract: Methods and apparatus to transmit and receive information bits encoded in duobinary, multilevel pulse-amplitude-modulated (PAM) optical signals are described. The transmitted optical signal has a narrow optical spectrum and a low symbol rate. Information bits are encoded in a M-ary PAM symbol sequence, where M≧2. The PAM symbol sequence is input to a finite-state machine, which yields an encoded sequence that changes sign between two symbol intervals when the encoded sequence takes on a nominally zero value during an odd number of intervening symbol intervals. The encoded sequence is lowpass filtered and modulated onto an optical electric field. The receiver processes a received optical electric field to obtain an electrical signal proportional to the received optical intensity, and performs M-ary symbol-by-symbol decisions to recover the transmitted information bits, without potential error propagation.

Abstract: Methods and apparatus to transmit and receive information bits encoded in duobinary, multilevel pulse-amplitude-modulated (PAM) optical signals are described. The transmitted optical signal has a narrow optical spectrum and a low symbol rate. Information bits are encoded in a M-ary PAM symbol sequence, where M≧2. The PAM symbol sequence is input to a finite-state machine, which yields an encoded sequence that changes sign between two symbol intervals when the encoded sequence takes on a nominally zero value during an odd number of intervening symbol intervals. The encoded sequence is lowpass filtered and modulated onto an optical electric field. The receiver processes a received optical electric field to obtain an electrical signal proportional to the received optical intensity, and performs M-ary symbol-by-symbol decisions to recover the transmitted information bits, without potential error propagation.

Abstract: Methods and apparatus to transmit and receive information bits encoded in duobinary, multilevel pulse-amplitude-modulated (PAM) optical signals. The transmitted optical signal has a narrow optical spectrum and a low symbol rate. Information bits are encoded in a M-ary PAM symbol sequence, where M≳2. A subtraction-based encoder precodes and duobinary filters the M-ary PAM symbol sequence, yielding an encoded sequence. The encoded sequence is lowpass filtered and modulated onto an optical electric field. The receiver processes a received optical electric field to obtain an electrical signal proportional to the received optical intensity, and performs M-ary symbol-by-symbol decisions to recover the transmitted information bits, without potential error propagation.

Abstract: Methods and apparatus to transmit and receive information bits encoded in duobinary, multilevel pulse-amplitude-modulated (PAM) optical signals are described. The transmitted optical signal has a narrow optical spectrum and a low symbol rate. Information bits are encoded in a M-ary PAM symbol sequence, where M≧3. The subsequence-based encoder decomposes the PAM symbol sequence into M1 subsequences, precodes each subsequence, performs duobinary filtering on each precoded subsequence, and forms a weighted sum of the duobinary precoded subsequences. The weighted sum of duobinary precoded subsequences is lowpass filtered and modulated onto an optical electric field. The receiver processes a received optical electric field to obtain an electrical signal proportional to the received optical intensity, and performs M-ary symbol-by-symbol decisions to recover the transmitted information bits, without potential error propagation.

Abstract: Methods and apparatus to transmit and receive information bits encoded in duobinary, multilevel pulse-amplitude-modulated (PAM) optical signals are described. The transmitted optical signal has a narrow optical spectrum and a low symbol rate. Information bits are encoded in a M-ary PAM symbol sequence, where M≧2. The PAM symbol sequence is input to a finite-state machine, which yields an encoded sequence that changes sign between two symbol intervals when the encoded sequence takes on a nominally zero value during an odd number of intervening symbol intervals. The encoded sequence is lowpass filtered and modulated onto an optical electric field. The receiver processes a received optical electric field to obtain an electrical signal proportional to the received optical intensity, and performs M-ary symbol-by-symbol decisions to recover the transmitted information bits, without potential error propagation.