A Fast and Low-Complexity Operator for the Computation of the Arctangent of a Complex Number

[EN] The computation of the arctangent of a complex number, i.e., the atan2 function, is frequently needed in hardware systems that could profit from an optimized operator. In this brief, we present a novel method to compute the atan2 function and a hardware architecture for its implementation. The method is based on a first stage that performs a coarse approximation of the atan2 function and a second stage that improves the output accuracy by means of a lookup table. We present results for fixed-point implementations in a field-programmable gate array device, all of them guaranteeing last-bit accuracy, which provide an advantage in latency, speed, and use of resources, when compared with well-established fixed-point options.This work was supported by the Spanish Ministerio de Economia y Competitividad and FEDER under Grant TEC2015-70858-C2-2-R.Torres Carot, V.; Valls Coquillat, J. (2017). A Fast and Low-Complexity Operator for the Computation of the Arctangent of a Complex Number. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 25(9):2663-2667. https://doi.org/10.1109/TVLSI.2017.2700519S2663266725

Fast- and Low-Complexity atan2(a,b) Approximation

[EN] This article presents a new entry to the class of published algorithms for the fast computation of the arctangent of a complex number. Our method uses a look-up table (LUT) to reduce computational errors. We also show how to convert a large-sized LUT addressed by two variables to an equivalent-performance smaller-sized LUT addressed by only one variable. In addition, we demonstrate how and why the use of follow-on LUTs applied to other simple arctan algorithms produce unexpected and interesting results.This work is funded by the Spanish Ministerio de Economía y Competitividad and FEDER under grant TEC2015-70858-C2-2-R.Torres Carot, V.; Valls Coquillat, J.; Lyons, R. (2017). Fast- and Low-Complexity atan2(a,b) Approximation. IEEE Signal Processing Magazine. 34(6):164-169. https://doi.org/10.1109/MSP.2017.2730898S16416934

FPGA implementation of a 10 GS/s variable-length FFT for OFDM-based optical communication systems

[EN] The transmission rate in current passive optical networks can be increased by employing Orthogonal Frequency Division Multiplexing (OFDM) modulation. The computational kernel of this modulation is the fast Fourier transform (FFT) operator, which has to achieve a very high throughput in order to be used in optical networks. This paper presents the implementation in an FPGA device of a variable-length FFT that can be configured in run-time to compute different FFT lengths between 16 and 1024 points. The FFT reaches a throughput of 10 GS/s in a Virtex-7 485T-3 FPGA device and was used to implement a 20 Gb/s optical OFDM receiver. (C) 2018 Elsevier B.V. All rights reserved.This work was supported by the Spanish Ministerio de Economia y Competitividad under project TEC2015-70858-C2-2-R with FEDER funds.Bruno, JS.; Almenar Terre, V.; Valls Coquillat, J. (2019). FPGA implementation of a 10 GS/s variable-length FFT for OFDM-based optical communication systems. Microprocessors and Microsystems. 64:195-204. https://doi.org/10.1016/j.micpro.2018.12.002S1952046

Optimised CORDIC-based atan2 computation for FPGA implementations

This paper is a postprint of a paper submitted to and accepted for publication in Electronics Letters and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at IET Digital Library[EN] A method for the implementation of the atan2 operator based on the coordinate rotation digital computer algorithm is described. In the proposal, the computation of the z-path takes advantage of the look-up table-based FPGA resources to reduce by between 17 and 25%, without performance deterioration, the overall area of the unrolled architecture.This work was funded by the Spanish Ministerio de Economia y Competitividad and FEDER under the grant TEC2015-70858-C2-2-R.Torres Carot, V.; Valls Coquillat, J.; Canet Subiela, MJ. (2017). Optimised CORDIC-based atan2 computation for FPGA implementations. Electronics Letters. 53(19):1296-1298. https://doi.org/10.1049/el.2017.2090S12961298531

Reduction of Complexity for Nonbinary LDPC Decoders With Compressed Messages

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this brief, a method for compressing the messages between check nodes and variable nodes is proposed. This method is named compressed nonbinary message passing (CNBMP). CNBMP reduces the number of messages exchanged between one check node and the connected variable nodes from d(c) x q to 5 x q, and its application has a high impact on the performance of the decoder: the storage and routing areas are reduced and the throughput is increased. Unlike other methods, CNBMP does not introduce any approximation or modification in the information and the processed operations are exactly the same as those of the original decoders; hence, no performance degradation is introduced. To demonstrate its advantages, an architecture applying this CNBMP to the Trellis Min-Max algorithm was derived showing that most of the storage resources were also reduced from dc x q to 5 x q. This architecture was implemented for a (837 726) nonbinary low-density parity-check code using a 90-nm CMOS technology reaching a throughput of 981 Mb/s with an area of 10.67 mm(2), which is 3.9 more efficient than the best solution found in the literature.This work was supported by the Spanish Ministerio de Ciencia e Innovacion under Grant TEC2011-27916. The work of F. Garcia-Herrero was supported by the Spanish Ministerio de Educacion through Formacion de Profesorado Universitario (FPU) under Grant AP2010-5178.Lacruz Jucht, JO.; García Herrero, FM.; Valls Coquillat, J. (2015). Reduction of Complexity for Nonbinary LDPC Decoders With Compressed Messages. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 23(11):2676-2679. https://doi.org/10.1109/TVLSI.2014.2377194S26762679231

Low-Complexity Time Synchronization Algorithm for Optical OFDM PON System Using a Directly Modulated DFB Laser

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper a low-complexity time synchronization algorithm for optical orthogonal frequency division multiplexing (OFDM) is proposed. The algorithm is based on a repetitive preamble that allows the use of a short cross correlator with an exponential average filter for postprocessing before a threshold detection. The signals in the correlation have been quantized with 1 bit, and the correlations have been implemented as a hard-wired tree adder to reduce the hardware cost. This solution has been verified in a passive optical network (PON) system using a directly modulated distributed feedback (DFB) laser achieving excellent performance with low computing processing complexity even in low signal-to-noise ratio scenarios. Finally, a parallel hardware architecture has been proposed for this time synchronization algorithm, and it has been implemented in a field programmable gate array device reaching a sample rate throughput up to 7.4 Gs/s.This work was supported by the Spanish Ministerio de Economia y Competitividad under projects TEC2012-38558-C02-02 and TEC2012-38558-C02-01 and with FEDER funds.Bruno, JS.; Almenar Terre, V.; Valls Coquillat, J.; Corral, JL. (2015). Low-Complexity Time Synchronization Algorithm for Optical OFDM PON System Using a Directly Modulated DFB Laser. IEEE/OSA Journal of Optical Communications and Networking. 7(11):1025-1033. doi:10.1364/JOCN.7.001025S1025103371

One minimum only trellis decoder for non-binary low-density parity-check codes

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.A one minimum only decoder for Trellis-EMS (OMO T-EMS) and for Trellis-Min-max (OMO T-MM) is proposed in this paper. In this novel approach, we avoid computing the second minimum in messages of the check node processor, and propose efficient estimators to infer the second minimum value. By doing so, we greatly reduce the complexity and at the same time improve latency and throughput of the derived architectures compared to the existing implementations of EMS and Min-max decoders. This solution has been applied to various NB-LDPC codes constructed over different Galois fields and with different degree distributions showing in all cases negligible performance loss compared to the ideal EMS and Min-max algorithms. In addition, two complete decoders for OMO T-EMS and OMO T-MM were implemented for the (837,726) NB-LDPC code over GF(32) for comparison proposals. A 90 nm CMOS process was applied, achieving a throughput of 711 Mbps and 818 Mbps respectively at a clock frequency of 250 MHz, with an area of 19.02 ${rm mm}^{2}$ and 16.10 ${rm mm}^{2}$ after place and route. To the best knowledge of the authors, the proposed decoders have higher throughput and area-time efficiency than any other solution for high-rate NB-LDPC codes with high Galois field order.This work was supported in part by the Spanish Ministerio de Ciencia e Innovacion under Grant TEC2011-27916 and in part by the Universitat Politecnica de Valencia under Grant PAID-06-2012-SP20120625. The work of F. Garcia-Herrero was supported by the Spanish Ministerio de Educacion under Grant AP2010-5178. David Declercq has been funded by the Institut Universitaire de France for this project. This paper was recommended by Associate Editor Z. Zhang.Lacruz, JO.; García Herrero, FM.; Valls Coquillat, J.; Declercq, D. (2015). One minimum only trellis decoder for non-binary low-density parity-check codes. IEEE Transactions on Circuits and Systems I: Regular Papers. 62(1):177-184. https://doi.org/10.1109/TCSI.2014.2354753S17718462

A Computational Efficient Nyquist Shaping Approach for Short-Reach Optical Communications

[EN] Recently, Half-Cycle Nyquist Subcarrier Modulation (HC-SCM) was proposed to achieve high spectral efficiency in intensity-modulator direct-detection optical links. This paper shows that the HC-SCM scheme has a high computational load and proposes the rational Oversampled Subcarrier Modulation (OVS-SCM) as a computational efficient alternative that, furthermore, improves the spectral efficiency. The presented experimental results show that our 256-QAM proposal allows to transmit below the hard-decision forward error correction, with a throughput of 17.8 Gb/s in a 2.5 GHz bandwidth, and a spectral efficiency of 7.2 b/s/Hz, through 20 km of single-mode optical fiber.This work was supported by the Spanish Ministerio de Economia y Competitividad and FEDER under the Grant TEC2015-70858-C2-2-R and Grant RTI2018-101658-B-I00.Pérez Pascual, MA.; Bruno, JS.; Almenar Terre, V.; Valls Coquillat, J. (2020). A Computational Efficient Nyquist Shaping Approach for Short-Reach Optical Communications. Journal of Lightwave Technology (Online). 38(7):1651-1658. https://doi.org/10.1109/JLT.2019.2961506S1651165838

Simplified trellis min-max decoder architecture for nonbinary low-density parity-check codes

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Nonbinary low-density parity-check (NB-LDPC) codes have become an efficient alternative to their binary counterparts in different scenarios, such as moderate codeword lengths, high-order modulations, and burst error correction. Unfortunately, the complexity of NB-LDPC decoders is still too high for practical applications, especially for the check node (CN) processing, which limits the maximum achievable throughput. Although a great effort has been made in the recent literature to overcome this disadvantage, the proposed decoders are still not ready for high-speed implementations for high-order fields. In this paper, a simplified trellis min max algorithm is proposed, where the CN messages are computed in a parallel way using only the most reliable information. The proposed CN algorithm is implemented using a horizontal layered schedule. The overall decoder architecture has been implemented in a 90-nm CMOS process for a ((N=837) and (K=726)) NB-LDPC code over GF(32), achieving a throughput of 660 Mb/s at nine iterations based on postlayout results. This decoder increases hardware efficiency compared with the existing recent solutions for the same code.This work was supported in part by the Spanish Ministerio de Ciencia e Innovacion under Grant TEC2011-27916; in part by the Universitat Politecnica de Valencia, Gandia, Spain, under Grant PAID-06-2012-SP20120625; and in part by the Institut Universitaire de France, Rennes, France. The work of F. Garcia-Herrero was supported in part by the Spanish Ministerio de Educacion under Grant AP2010-5178 and in part by the Institute Universitaire de France.Lacruz Jucht, JO.; García Herrero, FM.; Declercq, D.; Valls Coquillat, J. (2015). Simplified trellis min-max decoder architecture for nonbinary low-density parity-check codes. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 23(9):1783-1792. https://doi.org/10.1109/TVLSI.2014.2344113S1783179223

Hardware Architecture of a QAM Receiver for Short-Range Optical Communications

[EN] Short-reach optical fiber communications systems aim to achieve high throughput, in the order of tens of Gbps. The implementation of these high-speed systems requires parallel processing, which makes low-complexity designs of their subsystems a key to the successful large-scale deployment of this technology. Half-Cycle Nyquist Subcarrier Modulation (HC-SCM) was originally suggested for these systems with the goal of using as much bandwidth as possible and, therefore, achieving high communication rates. Recently, Oversampled Subcarrier Modulation (OVS-SCM) was proposed as an alternative more computational efficient than HC-SCM and also with a better spectral efficiency. This paper proposes a hardware-efficient architecture for an OVS-SCM receiver, which takes into account the inherent parallel processing of these systems. This receiver takes 16 samples in parallel from a 5 GSa/s analog-to-digital converter with a 3.2 GHz 3 dB bandwidth. Design solutions for the frame detection block, the mixer, the resampler, the fractional interpolator, the matched filter and the timing estimator are presented. Our results show that, compared to the HC-SCM receiver, this proposal reduces the computational load of the downconverter stages by 90%. FPGA implementation results are given to demonstrate that our proposal can be implemented in state-of-the-art devices.This work was supported in part by MCIN/AEI/10.13039/501100011033 under Grants RTI2018-101658-B100 and PID2021-126514OB-I00, and in part by the European Union through "ERDF Away of making Europe."Valls Coquillat, J.; Torres Carot, V.; Pérez Pascual, MA.; Almenar Terre, V. (2023). Hardware Architecture of a QAM Receiver for Short-Range Optical Communications. Journal of Lightwave Technology. 41(2):451-461. https://doi.org/10.1109/JLT.2022.321735745146141