Vahid Aref

Spatially Coupled Soft-Decision Error Correction for Future Lightwave Systems

In this paper, we discuss and present some recent advances in the field of error correcting codes and discuss their applicability for lightwave transmission systems. We introduce several classes of spatially coupled codes and discuss several design options for spatially coupled codes and show how rapidly decodable codes can be constructed by careful selection of the degree distribution. We confirm the good performance of some spatially coupled codes at very low bit error rates using an FPGA-based simulation. Finally, we compare all proposed schemes and show how spatially coupled Low-Density Parity-Check (LDPC) codes outperform conventional LDPC and polar codes with similar receiver complexity and memory requirements.

Experimental demonstration of nonlinear frequency division multiplexed transmission

We experimentally demonstrate an NFDM optical system with modulation over nonlinear discrete spectrum. Particularly, each symbol carries 4-bits from multiplexing two eigenvalues modulated by QPSK constellation. We show a low error performance using NFT detection with 4Gbps rate over 640km.

Approaching the Rate-Distortion Limit With Spatial Coupling, Belief Propagation, and Decimation

We investigate an encoding scheme for lossy compression of a binary symmetric source based on simple spatially coupled low-density generator-matrix codes. The degree of the check nodes is regular and the one of code-bits is Poisson distributed with an average depending on the compression rate. The performance of a low complexity belief propagation guided decimation algorithm is excellent. The algorithmic rate-distortion curve approaches the optimal curve of the ensemble as the width of the coupling window grows. Moreover, as the check degree grows both curves approach the ultimate Shannon rate-distortion limit. The belief propagation guided decimation encoder is based on the posterior measure of a binary symmetric test-channel. This measure can be interpreted as a random Gibbs measure at a temperature directly related to the noise level of the test-channel. We investigate the links between the algorithmic performance of the belief propagation guided decimation encoder and the phase diagram of this Gibbs measure. The phase diagram is investigated thanks to the cavity method of spin glass theory which predicts a number of phase transition thresholds. In particular, the dynamical and condensation phase transition temperatures (equivalently test-channel noise thresholds) are computed. We observe that: 1) the dynamical temperature of the spatially coupled construction saturates toward the condensation temperature and 2) for large degrees the condensation temperature approaches the temperature (i.e., noise level) related to the information theoretic Shannon test-channel noise parameter of rate-distortion theory. This provides heuristic insight into the excellent performance of the belief propagation guided decimation algorithm. This paper contains an introduction to the cavity method.

Next Generation Error Correcting Codes for Lightwave Systems

In this paper, we discuss and present some recent advances in the field of error correcting codes and discuss their applicability for lightwave transmission systems. We compare polar codes and spatially coupled codes and present recent modifications of the latter.

Spatially coupled codes and optical fiber communications: An ideal match?

In this paper, we highlight the class of spatially coupled codes and discuss their applicability to long-haul and submarine optical communication systems. We first demonstrate how to optimize irregular spatially coupled LDPC codes for their use in optical communications with limited decoding hardware complexity and then present simulation results with an FPGA-based decoder where we show that very low error rates can be achieved and that conventional block-based LDPC codes can be outperformed. In the second part of the paper, we focus on the combination of spatially coupled LDPC codes with different demodulators and detectors, important for future systems with adaptive modulation and for varying channel characteristics. We demonstrate that SC codes can be employed as universal, channel-agnostic coding schemes.

On spectral phase estimation of noisy solitonic transmission

We consider the coherent transmission of soliton pulses over a long noisy optical link. We propose an efficient estimation of the transmitted nonlinear spectral phase based on Minimum Mean Square Error estimation of the eigenvalues trajectory.

Triggering wave-like convergence of tail-biting spatially coupled LDPC codes

Spatially coupled low-density parity-check (SC-LDPC) codes can achieve the channel capacity under low-complexity belief propagation (BP) decoding, however, there is a non-negligible rate-loss because of termination effects for practical finite coupling lengths. In this paper, we study how we can approach the performance of terminated SC-LDPC codes by random shortening of tail-biting SC-LDPC codes. We find the minimum required rate-loss in order to achieve the same performance than terminated codes. We additionally study the use of tail-biting SC-LDPC codes for transmission over parallel channels (e.g., bit-interleaved-coded-modulation (BICM)) and investigate how the distribution of the coded bits between two parallel channels can change the performance of the code. We show that a tail-biting SC-LDPC code can be used with BP decoding almost anywhere within the achievable region of MAP decoding. The optimization comes with a mandatory buffer at the encoder side. We evaluate different distributions of coded bits in order to reduce this buffer length.

Practical implementation of nonlinear fourier transform based optical nonlinearity mitigation

This tutorial provides an introduction into the application of NFT in coherent transmission systems. It summarizes concepts for modulation, transmission, and detection of signals nonlinear spectrum with an emphasis on experimental realization.

Collision of QPSK modulated solitons

We study an isolated soliton collision of two QPSK modulated 1st order solitons having 12GHz frequency offset in simulation and experiment. Separate and joint NFT is applied to the received signals to show effects of the collision.

Spatially Coupled LDPC codes affected by a single random burst of erasures

Spatially-Coupled LDPC (SC-LDPC) ensembles achieve the capacity of binary memoryless channels (BMS), asymptotically, under belief-propagation (BP) decoding. In this paper, we study the BP decoding of these code ensembles over a BMS channel and in the presence of a single random burst of erasures. We show that in the limit of code length, codewords can be recovered successfully if the length of the burst is smaller than some maximum recoverable burst length. We observe that the maximum recoverable burst length is practically the same if the transmission takes place over binary erasure channel or over binary additive white Gaussian channel with the same capacity. Analyzing the stopping sets, we also estimate the decoding failure probability (the error floor) when the code length is finite.