Luis Salamanca

High Symbol Rate Coherent Optical Transmission Systems: 80 and 107 Gbaud

We demonstrate high speed optical transmission systems using digital coherent detection at all-electronically multiplexed symbol rates of 80 and 107 Gbaud. At 107 Gbaud, we demonstrate a single-carrier polarization division multiplexed quadrature phase shift keyed (PDM-QPSK) line rate of 428 Gb/s. At 80 Gbaud, we achieve a single-carrier line rate of 640 Gb/s using PDM 16-ary quadrature amplitude modulation (16-QAM). Using two optical subcarriers, we demonstrate a 1-Tb/s optical interface and conduct long-haul wavelength-division multiplexed (WDM) transmission on a 200-GHz grid over 3200 km of ultra-large effective area fiber.

Bayesian Equalization for LDPC Channel Decoding

We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbols posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver.

Near the Cramér–Rao Bound Precoding Algorithms for OFDM Blind Channel Estimation

The authors present a blind channel estimation of cyclic prefix (CP) orthogonal frequency-division multiplexing (OFDM) systems with nonredundant precoding based on second-order statistics. The study analyzes first the mean square error for the estimation of the covariance matrix of the received symbols. We prove that, for high and medium signal-to-noise ratios (SNRs), the estimation error in the diagonal entries of the covariance matrix exhibits a lower error than that in the off-diagonal elements. This behavior holds for SNR values in digital communication. Contrary to general belief, we prove that the diagonal of this matrix can be used for channel estimation. Hence, we develop a novel algorithm that utilizes this result. We also develop a low-complexity version that provides acceptable results with reduced computational requirements. Finally, we analyze the covariance matrix and propose another new algorithm with noise suppression capabilities. Some experimental results for Rayleigh channels are included to support these conclusions. In addition, they illustrate better performance of the new methods, compared with previous proposals and with the Cramér-Rao bound (CRB).

Transmission of 130-Gb/s PDM-QPSK over 5,760-km with co-propagating 10-Gb/s OOK channels in dispersion-managed NZDSF spans with soft-decision LDPCC coding

We transmit one 130-Gb/s PDM-QPSK channel surrounded by fifteen 10-Gb/s OOK channels at 50-GHz channel spacing over 5,760 km in dispersion-managed TrueWave® REACH spans, with a 20% overhead concatenated FEC scheme using soft-decision LDPCC coding.

Tree Expectation Propagation for ML Decoding of LDPC Codes over the BEC

We propose a decoding algorithm for LDPC codes that achieves the maximum likelihood (ML) solution over the binary erasure channel (BEC). In this channel, the tree-structured expectation propagation (TEP) decoder improves the peeling decoder (PD) by processing check nodes of degree one and two. However, it does not achieve the ML solution, as the tree structure of the TEP allows only for approximate inference. In this paper, we provide the procedure to construct the structure needed for exact inference. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), modifies the code graph by recursively eliminating any check node and merging this information in the remaining graph. The GTEP decoder upon completion either provides the unique ML solution or a tree graph in which the number of parent nodes indicates the multiplicity of the ML solution. We also explain the algorithm as a Gaussian elimination method, relating the GTEP to other ML solutions. Compared to previous approaches, it presents an equivalent complexity, it exhibits a simpler graphical message-passing procedure and, most interesting, the algorithm can be generalized to other channels.

Tree-Structured Expectation Propagation for LDPC Decoding over BMS Channels

In this paper, we put forward the tree-structured expectation propagation (TEP) algorithm for decoding block and convolutional low-density parity-check codes over any binary channel. We have already shown that TEP improves belief propagation (BP) over the binary erasure channel (BEC) by imposing marginal constraints over a set of pairs of variables that form a tree or a forest. The TEP decoder is a message-passing algorithm that sequentially builds a tree/forest of erased variables to capture additional information disregarded by the standard BP decoder, which leads to a noticeable reduction of the error rate for finite-length codes. In this paper, we show how the TEP can be extended to any channel, specifically to binary memoryless symmetric (BMS) channels. We particularly focus on how the TEP algorithm can be adapted for any channel model and, more importantly, how to choose the tree/forest to keep the gains observed for block and convolutional LDPC codes over the BEC.

Approaching the DT Bound Using Linear Codes in the Short Blocklength Regime

The dependence-testing (DT) bound is one of the strongest achievability bounds for the binary erasure channel (BEC) in the finite block length regime. In this paper, we show that maximum likelihood decoded regular low-density parity-check (LDPC) codes with at least 5 ones per column almost achieve the DT bound. Specifically, using quasi-regular LDPC codes with block length of 256 bits, we achieve a rate that is less than 1% away from the rate predicted by the DT bound for a word error rate below

Tree-structured expectation propagation for LDPC decoding over the AWGN channel

10^{-3}

On the Design of LDPC-Convolutional Ensembles Using the TEP Decoder

. The results also indicate that the maximum-likelihood solution is computationally feasible for decoding block codes over the BEC with several hundred bits.

Finite-length analysis of the TEP decoder for LDPC ensembles over the BEC

In this paper, we propose the tree-structured expectation propagation (TEP) algorithm for low-density parity-check (LDPC) decoding over the additive white Gaussian noise (AWGN) channel. By imposing a tree-like approximation over the graphical model of the code, this algorithm introduces pairwise marginal constraints over pairs of variables, which provide joint information of the variables related. Thanks to this, the proposed TEP decoder improves the performance of the standard belief propagation (BP) solution. An efficient way of constructing the tree-like structure is also described. The simulation results illustrate the TEP decoder gain in the finite-length regime, compared to the standard BP solution. For code lengths shorter than n = 512, the gain in the waterfall region achieves up to 0.25 dB. We also notice a remarkable reduction of the error floor.