Replacing the Soft FEC Limit Paradigm in the Design of Optical Communication Systems

The FEC limit paradigm is the prevalent practice for designing optical communication systems to attain a certain bit-error rate (BER) without forward error correction (FEC). This practice assumes that there is an FEC code that will reduce the BER after decoding to the desired level. In this paper, we challenge this practice and show that the concept of a channel-independent FEC limit is invalid for soft-decision bit-wise decoding. It is shown that for low code rates and high order modulation formats, the use of the soft FEC limit paradigm can underestimate the spectral efficiencies by up to 20%. A better predictor for the BER after decoding is the generalized mutual information, which is shown to give consistent post-FEC BER predictions across different channel conditions and modulation formats. Extensive optical full-field simulations and experiments are carried out in both the linear and nonlinear transmission regimes to confirm the theoretical analysis

On Achievable Rates for Long-Haul Fiber-Optic Communications

Lower bounds on mutual information (MI) of long-haul optical fiber systems for hard-decision and soft-decision decoding are studied. Ready-to-use expressions to calculate the MI are presented. Extensive numerical simulations are used to quantify how changes in the optical transmitter, receiver, and channel affect the achievable transmission rates of the system. Special emphasis is put to the use of different quadrature amplitude modulation formats, channel spacings, digital back-propagation schemes and probabilistic shaping. The advantages of using MI over the prevailing $Q$-factor as a figure of merit of coded optical systems are also highlighted.Comment: Hard decision mutual information analysis added, two typos correcte

Soft-Decision Low-Complexity Chase Decoders for the RS(255,239) Code

[EN] In this work, we present a new architecture for soft-decision Reed-Solomon (RS) Low-Complexity Chase (LCC) decoding. The proposed architecture is scalable and can be used for a high number of test vectors. We propose a novel Multiplicity Assignment stage that sorts and stores only the location of the errors inside the symbols and the powers of a that identify the positions of the symbols in the frame. Novel schematics for the Syndrome Update and Symbol Modification blocks that are adapted to the proposed sorting stage are also presented. We also propose novel solutions for the problems that arise when a high number of test vectors is processed. We implemented three decoders: a h = 4 LCC decoder and two decoders that only decode 31 and 60 test vectors of true h = 5 and h = 6 LCC decoders, respectively. For example, our h = 4 decoder requires 29% less look-up tables in Virtex-V Field Programmable Gate Array (FPGA) devices than the best soft-decision RS decoder published to date, while has a 0.07 dB coding gain over that decoder.This research was funded by the Spanish Ministerio de Economia y Competitividad and FEDER grant number TEC2015-70858-C2-2-RTorres Carot, V.; Valls Coquillat, J.; Canet Subiela, MJ.; García Herrero, FM. (2019). Soft-Decision Low-Complexity Chase Decoders for the RS(255,239) Code. Electronics. 8(1):1-13. https://doi.org/10.3390/electronics8010010S11381Cideciyan, R., Gustlin, M., Li, M., Wang, J., & Wang, Z. (2013). Next generation backplane and copper cable challenges. IEEE Communications Magazine, 51(12), 130-136. doi:10.1109/mcom.2013.6685768Koetter, R., & Vardy, A. (2003). Algebraic soft-decision decoding of reed-solomon codes. IEEE Transactions on Information Theory, 49(11), 2809-2825. doi:10.1109/tit.2003.819332Sudan, M. (1997). Decoding of Reed Solomon Codes beyond the Error-Correction Bound. Journal of Complexity, 13(1), 180-193. doi:10.1006/jcom.1997.0439Guruswami, V., & Sudan, M. (1999). Improved decoding of Reed-Solomon and algebraic-geometry codes. IEEE Transactions on Information Theory, 45(6), 1757-1767. doi:10.1109/18.782097Jiang, J., & Narayanan, K. R. (2008). Algebraic Soft-Decision Decoding of Reed–Solomon Codes Using Bit-Level Soft Information. IEEE Transactions on Information Theory, 54(9), 3907-3928. doi:10.1109/tit.2008.928238Jiangli Zhu, Xinmiao Zhang, & Zhongfeng Wang. (2009). Backward Interpolation Architecture for Algebraic Soft-Decision Reed–Solomon Decoding. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 17(11), 1602-1615. doi:10.1109/tvlsi.2008.2005575Jiangli Zhu, & Xinmiao Zhang. (2008). Efficient VLSI Architecture for Soft-Decision Decoding of Reed–Solomon Codes. IEEE Transactions on Circuits and Systems I: Regular Papers, 55(10), 3050-3062. doi:10.1109/tcsi.2008.923169Zhongfeng Wang, & Jun Ma. (2006). High-Speed Interpolation Architecture for Soft-Decision Decoding of Reed–Solomon Codes. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 14(9), 937-950. doi:10.1109/tvlsi.2006.884046Zhang, X. (2006). Reduced Complexity Interpolation Architecture for Soft-Decision Reed–Solomon Decoding. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 14(10), 1156-1161. doi:10.1109/tvlsi.2006.884177Xinmiao Zhang, & Parhi, K. K. (2005). Fast factorization architecture in soft-decision Reed-Solomon decoding. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 13(4), 413-426. doi:10.1109/tvlsi.2004.842914Bellorado, J., & Kavcic, A. (2010). Low-Complexity Soft-Decoding Algorithms for Reed–Solomon Codes—Part I: An Algebraic Soft-In Hard-Out Chase Decoder. IEEE Transactions on Information Theory, 56(3), 945-959. doi:10.1109/tit.2009.2039073García-Herrero, F., Valls, J., & Meher, P. K. (2011). High-Speed RS(255, 239) Decoder Based on LCC Decoding. Circuits, Systems, and Signal Processing, 30(6), 1643-1669. doi:10.1007/s00034-011-9327-4Zhang, W., Wang, H., & Pan, B. (2013). Reduced-Complexity LCC Reed–Solomon Decoder Based on Unified Syndrome Computation. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 21(5), 974-978. doi:10.1109/tvlsi.2012.2197030Peng, X., Zhang, W., Ji, W., Liang, Z., & Liu, Y. (2015). Reduced-Complexity Multiplicity Assignment Algorithm and Architecture for Low-Complexity Chase Decoder of Reed-Solomon Codes. IEEE Communications Letters, 19(11), 1865-1868. doi:10.1109/lcomm.2015.2477495Lin, Y.-M., Hsu, C.-H., Chang, H.-C., & Lee, C.-Y. (2014). A 2.56 Gb/s Soft RS (255, 239) Decoder Chip for Optical Communication Systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 61(7), 2110-2118. doi:10.1109/tcsi.2014.2298282Wu, Y. (2015). New Scalable Decoder Architectures for Reed–Solomon Codes. IEEE Transactions on Communications, 63(8), 2741-2761. doi:10.1109/tcomm.2015.2445759Garcia-Herrero, F., Canet, M. J., Valls, J., & Meher, P. K. (2012). High-Throughput Interpolator Architecture for Low-Complexity Chase Decoding of RS Codes. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 20(3), 568-573. doi:10.1109/tvlsi.2010.210396

Bit error performance of diffuse indoor optical wireless channel pulse position modulation system employing artificial neural networks for channel equalisation

The bit-error rate (BER) performance of a pulse position modulation (PPM) scheme for non-line-of-sight indoor optical links employing channel equalisation based on the artificial neural network (ANN) is reported. Channel equalisation is achieved by training a multilayer perceptrons ANN. A comparative study of the unequalised `soft' decision decoding and the `hard' decision decoding along with the neural equalised `soft' decision decoding is presented for different bit resolutions for optical channels with different delay spread. We show that the unequalised `hard' decision decoding performs the worst for all values of normalised delayed spread, becoming impractical beyond a normalised delayed spread of 0.6. However, `soft' decision decoding with/without equalisation displays relatively improved performance for all values of the delay spread. The study shows that for a highly diffuse channel, the signal-to-noise ratio requirement to achieve a BER of 10−5 for the ANN-based equaliser is ~10 dB lower compared with the unequalised `soft' decoding for 16-PPM at a data rate of 155 Mbps. Our results indicate that for all range of delay spread, neural network equalisation is an effective tool of mitigating the inter-symbol interference

Achievable Information Rates for Coded Modulation with Hard Decision Decoding for Coherent Fiber-Optic Systems

We analyze the achievable information rates (AIRs) for coded modulation schemes with QAM constellations with both bit-wise and symbol-wise decoders, corresponding to the case where a binary code is used in combination with a higher-order modulation using the bit-interleaved coded modulation (BICM) paradigm and to the case where a nonbinary code over a field matched to the constellation size is used, respectively. In particular, we consider hard decision decoding, which is the preferable option for fiber-optic communication systems where decoding complexity is a concern. Recently, Liga \emph{et al.} analyzed the AIRs for bit-wise and symbol-wise decoders considering what the authors called \emph{hard decision decoder} which, however, exploits \emph{soft information} of the transition probabilities of discrete-input discrete-output channel resulting from the hard detection. As such, the complexity of the decoder is essentially the same as the complexity of a soft decision decoder. In this paper, we analyze instead the AIRs for the standard hard decision decoder, commonly used in practice, where the decoding is based on the Hamming distance metric. We show that if standard hard decision decoding is used, bit-wise decoders yield significantly higher AIRs than symbol-wise decoders. As a result, contrary to the conclusion by Liga \emph{et al.}, binary decoders together with the BICM paradigm are preferable for spectrally-efficient fiber-optic systems. We also design binary and nonbinary staircase codes and show that, in agreement with the AIRs, binary codes yield better performance.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201

Wavelet—Artificial Neural Network Receiver for Indoor Optical Wireless Communications

The multipath induced intersymbol interference (ISI) and fluorescent light interference (FLI) are the two most important system impairments that affect the performance of indoor optical wireless communication (OWC) systems. The presence of either incurs a high optical power penalty (OPP) and hence the interferences should be mitigated with suitable techniques to ensure optimum system performance. The discrete wavelet transform (DWT) and the artificial neural network (ANN) based receiver to mitigate the effect of FLI and ISI has been proposed in the previous study for the one-off keying (OOK) modulation scheme. It offers performance improvement compared to the traditional methods of employing a high pass filter (HPF) and a finite impulse response (FIR) equalizer. In this paper, the investigation of the DWT-ANN based receiver for baseband modulation techniques including OOK, pulse position modulation (PPM) and digital pulse interval modulation (DPIM) are reported. The proposed system is implemented using digital signal processing (DSP) board and results are verified by comparison with simulation data

Multidimensional Optimized Optical Modulation Formats

This chapter overviews the relatively large body of work (experimental and theoretical) on modulation formats for optical coherent links. It first gives basic definitions and performance metrics for modulation formats that are common in the literature. Then, the chapter discusses optimization of modulation formats in coded systems. It distinguishes between three cases, depending on the type of decoder employed, which pose quite different requirements on the choice of modulation format. The three cases are soft-decision decoding, hard-decision decoding, and iterative decoding, which loosely correspond to weak, medium, and strong coding, respectively. The chapter also discusses the realizations of the transmitter and transmission link properties and the receiver algorithms, including DSP and decoding. It further explains how to simply determine the transmitted symbol from the received 4D vector, without resorting to a full search of the Euclidean distances to all points in the whole constellation

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.Comment: Invited paper to be presented in the special session on "Signal Processing, Coding, and Information Theory for Optical Communications" at IEEE SPAWC 201

Improved Decoding of Staircase Codes: The Soft-aided Bit-marking (SABM) Algorithm

Staircase codes (SCCs) are typically decoded using iterative bounded-distance decoding (BDD) and hard decisions. In this paper, a novel decoding algorithm is proposed, which partially uses soft information from the channel. The proposed algorithm is based on marking certain number of highly reliable and highly unreliable bits. These marked bits are used to improve the miscorrection-detection capability of the SCC decoder and the error-correcting capability of BDD. For SCCs with $2$-error-correcting Bose-Chaudhuri-Hocquenghem component codes, our algorithm improves upon standard SCC decoding by up to $0.30$~dB at a bit-error rate (BER) of $10^{-7}$. The proposed algorithm is shown to achieve almost half of the gain achievable by an idealized decoder with this structure. A complexity analysis based on the number of additional calls to the component BDD decoder shows that the relative complexity increase is only around $4\%$ at a BER of $10^{-4}$. This additional complexity is shown to decrease as the channel quality improves. Our algorithm is also extended (with minor modifications) to product codes. The simulation results show that in this case, the algorithm offers gains of up to $0.44$~dB at a BER of $10^{-8}$.Comment: 10 pages, 12 figure

Performance Prediction of Nonbinary Forward Error Correction in Optical Transmission Experiments

In this paper, we compare different metrics to predict the error rate of optical systems based on nonbinary forward error correction (FEC). It is shown that the correct metric to predict the performance of coded modulation based on nonbinary FEC is the mutual information. The accuracy of the prediction is verified in a detailed example with multiple constellation formats, FEC overheads in both simulations and optical transmission experiments over a recirculating loop. It is shown that the employed FEC codes must be universal if performance prediction based on thresholds is used. A tutorial introduction into the computation of the threshold from optical transmission measurements is also given.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog