Frequency-domain adaptive MIMO filter with fractional oversampling using stochastic gradient descent for long-haul transmission over coupled 4-core fibers: erratum.

This erratum corrects errors in Fig. 9(b) and Fig. 14 of our published paper [Opt.

Frequency-domain adaptive MIMO filter with fractional oversampling using stochastic gradient descent for long-haul transmission over coupled 4-core fibers.

We propose a fractionally spaced frequency-domain adaptive multi-input multi-output (MIMO) filter architecture in which the sampling rate of input signals is below 2× oversampling with a non-integer oversampling factor for mode demultiplexing in long-haul transmission over coupled multi-core fibers. The frequency-domain sampling rate conversion to the symbol rate, i.e.

Compensation and monitoring of transmitter and receiver impairments in 10,000-km single-mode fiber transmission by adaptive multi-layer filters with augmented inputs.

We propose an adaptive multi-layer (ML) filter architecture to compensate for linear impairments that occur in transmitter (Tx) and receiver (Rx) components in ultra-long-haul optical fiber transmission systems, in which large chromatic dispersion (CD) accumulates in the received signal. The architecture consists of strictly linear (SL) and widely linear (WL) filter layers, and the coefficients of the ML filters are adaptively controlled by gradient calculation with back propagation and stochastic gradient descent. Static CD compensation is performed on the received signal and its complex conjugate before the adaptive ML filters.

Adaptive multi-layer filters incorporated with Volterra filters for impairment compensation including transmitter and receiver nonlinearity.

We propose a receiver-side signal processing to compensate for nonlinearity that occurs in transmitter (Tx) and receiver (Rx) components of coherent optical fiber transmission systems. Nonlinear effects in transmission systems are not mutually commutative with any linear effects in general. Considering the order in which all the relevant impairments occur, we adopt a multi-layer (ML) filter architecture.

Transmitter and receiver impairment monitoring using adaptive multi-layer linear and widely linear filter coefficients controlled by stochastic gradient descent.

We propose a monitoring method for individual impairments in a transmitter (Tx) and receiver (Rx) by using filter coefficients of multi-layer strictly linear (SL) and widely linear (WL) filters to compensate for relevant impairments where the filter coefficients are adaptively controlled by stochastic gradient descent with back propagation from the last layer outputs. Considering the order of impairments occurring in a Tx or Rx of coherent optical transmission systems and their non-commutativity, we derive a model relating in-phase (I) and quadrature (Q) skew, IQ gain imbalance, and IQ phase deviation in a Tx or Rx to the WL filter responses in our multi-layer filter architecture. We evaluated the proposed method through simulations using polarization-division multiplexed (PDM)-quadrature phase shift keying and a transmission experiment of 32-Gbaud PDM 64-quadrature amplitude modulation over a 100-km single-mode fiber span.

Adaptive equalization of transmitter and receiver IQ skew by multi-layer linear and widely linear filters with deep unfolding.

We propose a multi-layer cascaded filter architecture consisting of differently sized strictly linear (SL) and widely linear (WL) filters to compensate for the relevant linear impairments in optical fiber communications including in-phase/quadrature (IQ) skew in both transmitter and receiver by using deep unfolding. To control the filter coefficients adaptively, we adopt a gradient calculation with back propagation from machine learning with neural networks to minimize the magnitude of deviation of the filter outputs of the last layer from the desired state in a stochastic gradient descent (SGD) manner. We derive a filter coefficient update algorithm for multi-layer SL and WL multi-input multi-output finite-impulse response filters.

Wide range rate adaptation of QAM-based probabilistic constellation shaping using a fixed FEC with blind adaptive equalization.

We investigate the rate adaptability of quadrature amplitude modulation (QAM)-based probabilistic constellation shaping (PCS) using a fixed forward error correction (FEC) scheme over a wide range of information rates (IRs). Blind adaptive equalization that does not sacrifice any of the IRs was adopted. We show that the conventional decision directed least mean square (DDLMS) algorithm can cause a problem of mis-convergence when it is applied to the PCS of a low IR.

Performance of mode diversity reception of a polarization-division-multiplexed signal for free-space optical communication under atmospheric turbulence.

We investigated the performance of mode diversity reception of a polarization-division-multiplexed (PDM) signal with few-mode-fiber (FMF) coupling for high-speed free-space optical communications under atmospheric turbulence. Optical propagation through eigenmodes of a FMF yields coupling between different linearly polarized (LP) modes in orthogonal polarizations, which causes power imbalance and loss of the orthogonality of multiplexed signals within each individual LP mode. Due to this phenomenon, the architecture of mode diversity combining affects the receiver performance.

Storage and retrieval of a squeezed vacuum.

Storage and retrieval of a squeezed vacuum was successfully demonstrated using electromagnetically induced transparency. The squeezed vacuum pulse having a temporal width of 930 ns was incident on the laser cooled 87Rb atoms with an intense control light in a coherent state. When the squeezed vacuum pulse was slowed and spatially compressed in the cold atoms, the control light was switched off.

Ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency.

We have succeeded in observing ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency. Squeezed vacuum pulses (probe lights) were incident on a laser-cooled 87Rb gas together with an intense coherent light (control light). A homodyne method sensitive to the vacuum state was employed for detecting the probe pulse passing through the gas.