© 2017 IEEE. Achievable information rates are discussed as a tool to analyse and design optical networks. It is shown that the maximum throughput of the network and its dependency of different network parameters can be predicted with such a tool

Alvarado, A

Ives, DJ

Savory, SJ

English

Alex Alvarado

David J. Ives

Seb J. Savory

Crossref

Designing adaptive coded modulation for optical networks via achievable information rates

Achievable information rates are discussed as a tool to analyse and design optical networks. It is shown that the maximum throughput of the network and its dependency of different network parameters can be predicted with such a tool

Alvarado, A.

Ives, D.J.

Savory, S.J.

NARCIS 

Alvarado, A Alex

Ives, David J

Savory, Seb J

Repository TU/e

Pure OAI Repository

Apollo (Cambridge)

Designing Adaptive Coded Modulation for OpticalNetworks via Achievable Information RatesAlex Alvarado1, David J. Ives2, and Seb J. Savory21Signal Processing Systems (SPS) Group, Department of Electrical EngineeringEindhoven University of Technology (TU/e), 5600MB Eindhoven, The Netherlands2Department of Engineering, Electrical DivisionUniversity of Cambridge, CB3 0FA Cambridge, United Kingdome-mail: alex.alvarado@ieee.orgABSTRACTAchievable information rates are discussed as a tool to analyse and design optical networks. It is shown thatthe maximum throughput of the network and its dependency of different network parameters can be predictedwith such a tool.Keywords: Achievable information rates, information theory, network throughput, optical networks.1. INTRODUCTIONOptical networks utilise wavelength routing to transparently connect source and destination. Such networksare the backbone of the Internet and can be abstracted to a set of multiple point-to-point routes. These routescan vary considerably in length, and thus, the signal quality in optical networks—measured for example interms of signal-to-noise ratio (SNR)—can vary considerably. While the SNR in short routes is high, long routesthat connect nodes far apart experience low SNRs. This degradation is usually due to the accumulated noiseintroduced by amplifiers in the link as well as nonlinear distortion due to neighboring WDM channels.Future optical networks will be spectrally efficient, and thus, they will use multilevel modulation and forwarderror correction (FEC). This combination is known as coded modulation (CM) [1] and its design requires thejoint optimisation of the FEC and modulation format. Very often, CM receivers are implemented as a bit-wisereceiver [2]. Hard or soft information on the code bits is calculated first, and then, an FEC decoder is used [3].The most conservative CM design strategy for an optical network is to choose the transceiver to operate error-free on the worst route [4, p. 138]. Under this design paradigm, any route reconfiguration can be accommodatedthrough the network. However, this leads to over provisioning of resources, which has lead to an increasedinterest in networks with adaptive CM. In such a scenario, the modulation format and the FEC is varied tomatch the SNRs of the different routes. Other parameters that can be adapted include, e.g., frequency separation(flex-grid), launch power, rate, etc (see [5, Fig. 3]). The network resources can be better utilised if these degreesof freedom are jointly optimised in conjunction with the routing of the optical light path through the network.To increase the network throughput, different approaches have been investigated in the literature. For example,variable FEC, and variable modulation, and variable symbol rate [6]–[14]. Routing and spectrum assignment forflex-grid optical networks was studied in [15]. Nonlinear effects have been taken into account using the Gaussiannoise (GN) model [16]. In [17], the GN model was used to adapt the routing and wavelength assignmentproblem and later used in [18] to jointly optimise power, modulation format, and carrier frequencies (flex-grid).Numerical integration of the GN model was used in [19] to assess SNR and throughput optimisation via powerand modulation adaptation. This methodology was also used in [20], [21] to sequentially optimise modulationformat and power.An achievable information rate (AIR) is an information-theoretic quantity that quantifies the theoreticallymaximum data rate that can be reliably transmitted through a channel. AIRs directly shows the dependency ofthe data rate on the FEC coding rate (or equivalently, FEC overhead) and the modulation format. AIRs are wellunderstood for point-to-point links and can also be used to analyse the theoretically maximum throughput of anetwork. This was done for both hard-decision FEC (HD-FEC) and soft-decision FEC (SD-FEC) and differentnetwork topologies in [22]. We used the same methodology in [23] to study the effect of the amplifier noisefigure on the network throughput. In this paper we review this methodology and highlight its advantages andshortcomings. While for point-to-point links and an AWGN channel AIRs are determined by the SNR, we showthat for an optical network, the analysis depends on the SNR distribution of the routes.2. ACHIEVABLE INFORMATION RATES2.1 Point-to-point LinksThe capacity of the AWGN channel under an average power constraint is C = 2 log2(1 + SNR), where thepre-log factor of 2 takes into account the two polarisations. The value of C represents the maximum number ofinformation bits per symbol that can be reliably transmitted through an AWGN channel. The AWGN capacity is2achieved when the transmitted symbols are chosen from a zero-mean Gaussian distribution. In practice, however,the modulation has M discrete levels, which reduces the achievable transmission rates.We consider a CM transmitter where a FEC encoder generates code bits. These bits are gathered in groupsof m, and then mapped to a QAM constellation with 2m = M constellation points. These symbols are thentransmitted through a channel. At the receivers, two structures are considered. The first one is based on a HD-FEC decoder. In this case, the noisy symbols are first converted into bits (m bits per received symbol). Thesebits are passed to an HD-FEC decoder. In the second structure, the noisy symbols are converted into “soft” bits(usually log-likelihood ratios), which are then passed to an SD-FEC decoder.For HD-FEC, Shannon’s coding theorem states that error-free transmission is possible ifRc ≤ 1−Hb(BER) = 1 + BER · log2 BER + (1− BER) · log2 (1− BER), (1)where Rc is the rate of the FEC encoder, Hb(·) is the binary entropy function, and BER is the average pre-FECBER (across m bit positions). The AIR is therefore m(1−Hb(BER)) (in bit per symbol) and it represents themaximum number of bits that can be reliably transmitted in each symbol.The values of the AIRs m(1 − Hb(BER)) for M = 4, 16, . . . , 1024 are shown in Fig. 1 (left). The resultsare obtained for an AWGN channel and 2 polarisations. These AIRs cross each other for different values of M(see the asterisks in Fig. 1), and thus, the theoretically optimal choice of Rc and M is not straightforward. ForHD-FEC we consider here, QPSK should be used for SNRs below 5.8 dB, 16QAM for 5.8 ≤ SNR ≤ 14 dB,etc. The corresponding FEC OHs are shown in Fig. 1 (right). This figure also shows the optimum minimumand maximum OH values for each modulation format.−5 0 5 10 15 20 25 3005101520SNR [dB]AIR[bit/sym]Capacity CQPSK16QAM64QAM256QAM1024QAM−5 0 5 10 15 20 25 3010010110210315.67%5.85%2.85%1.68%1039.04%131.34%58.77%37.12%27.10%SNR [dB]FECOH%Figure 1. AIRs with HD-FEC (left) and corresponding OHs (right). The black asterisks show the SNR valueswhere the modulation size should be changed. The channel capacity C is shown for comparison.2.2 Optical NetworksThe performance metric under consideration is the total network throughput, which we denote by Θ. For aprecise definition of Θ, we refer the reader to [22, Sec. III]. The network throughput represents the total traffictransported by the network that satisfies a given traffic demand.To solve the network throughput problem, the routing and wavelength assignment problem was solvednumerically as an integer linear programming (ILP) problem as described in [21, Section 4.1]. In particular,we maximised the network throughput Θ under a uniform traffic demand assuming the transceivers achieve thechannel capacity C, and for a fixed channel separation (50 GHz). All other system parameters are given in [22,Table I]. The channel capacity C is pre-calculated based on the route SNR, which is in turn calculated usingthe GN model assuming a uniform launch power that maximises the SNR of the worst case central wavelengthchannel (see more details in [22, Sec. II-C]).The ILP solution provides the number of active light paths (i.e., number of transceivers) and their routesbetween each node pair. From this, the total number of active light paths T in the network is obtained.This solution also provides the SNR of each active light path. The obtained results are shown in Fig. 2for three network topologies: national (Deutsche Telekom Germany (DTG)), continental (NSF topology), andtranscontinental (Google B4 (GB4)). These networks are described in detail in [22, Sec. II-B]. The vertical barsshow the number of transceivers that need to be installed to maximise the network throughput. The total numberof transceivers for the DTG, NSF, and DTG networks are 1230, 1094, and 570, respectively.The vertical bars in Fig. 2 can be interpreted as the SNR distribution across the network. By comparing thesedistributions, it is clear that the average SNRs across the network decreases as the size of the network increases.30 5 10 15 20 25050100150200T = 1230Θ = 524 TbpsSNR [dB]NumberofTransceiversDTG Network0 5 10 15 20 2502040T = 1094Θ = 278 TbpsSNR [dB]NumberofTransceiversNSF Network0 5 10 15 20 250102030T = 570Θ = 88 TbpsSNR [dB]NumberofTransceiversGB4 NetworkFigure 2. Number of transceivers (vertical lines with triangles at the top) for all SNR values for the three networktopologies assuming all transceivers achieve the capacity C. Network throughputs Θ are also shown.This is due to the presence of long links in continental and transcontinental networks (NSF and GB4). The SNRdistributions in Fig. 2 also show that the spread of the SNR values is much larger for large networks. Whilefor the DTG network, the variation in SNR is about 10 dB, for the GB4 network, this variation is about 20 dB.Once the SNR values for the active light paths are found, the maximum network throughput can be calculatedusing AIRs. In particular, the SNRs of the light paths shown in Fig. 2 are first grouped for each source destinationpair. Then, the SNRs are “mapped” to throughputs AIR curves. In the ideal case when transceivers achieve thechannel capacity, the resulting throughputs are 524, 278, and 88 Tbps (see Fig. 2). For the more realistic caseof discrete constellations, this mapping approach can still be used, via the results in Fig. 1. This is shownschematically in Fig. 3 (left) for the DTG network. These idealised results show that the transceivers shouldonly use 64QAM and 256QAM. The results in Fig. 3 (right) show similar results for SD-FEC. In this case,AIRs similar to those in Fig. 1 can be obtained based on the generalised mutual information [2], [3]. The resultsin Fig. 3 (right) show how most of the transceivers should use 256QAM and 1024QAM (for the short routeswith high SNRs).−5 0 5 10 15 20 25 3005101520SNR [dB]AIR[bit/sym]Capacity CQPSK16QAM64QAM256QAM1024QAM−5 0 5 10 15 20 25 3005101520SNR [dB]AIR[bit/sym]Capacity CQPSK16QAM64QAM256QAM1024QAMFigure 3. Optimum modulation format for HD-FEC (left) and SD-FEC (right) as well as the SNR distributionfor the DTG network.2.3 Applications: Code Rates and Amplifier Noise FigureOne of the key components in an optical network are the EDFAs, which are characterised by their noise figure(NF). This NF varies between 3 dB (the theoretical minimum) and 5− 7 dB (for most commercially availableamplifiers). The results in the previous section were obtained for a NF of 5 dB. Here, we use the methodologydescribed above to quantify the dependency of the network throughout on the amplifier NF.The obtained results are shown in Fig. 4. For NF= 5 dB, the highlighted throughputs are those obtained inFig. 3 and show the potential gains offered by SD-FEC over HD-FEC. These result show that the gains offeredby SD-FEC are much more important in large networks. For example, the relative throughput gains for theDTG network are, on average, 13%; for the GB4 network these gains increase to 28%. The results in Fig. 4also show the tradeoff between SD-FEC and amplifier noise figure: for all three networks, a given throughputobtained with HD-FEC can be maintained if SD-FEC is implemented and the NF is increased by 3 dB.4Channel Capacity Ideal SD-FEC Ideal HD-FEC3 4 5 6 70200400600524Tbps489Tbps431TbpsAmplifier NF [dB]Throughput[Tbps]DTG Network3 4 5 6 70100200300278Tbps255Tbps217TbpsAmplifier NF [dB]Throughput[Tbps]NSF Network3 4 5 6 705010088Tbps81Tbps64TbpsAmplifier NF [dB]Throughput[Tbps]GB4 NetworkFigure 4. Network throughputs for three different network topologies as a function of the amplifier NF:transceivers achieving the channel capacity (black lines), SD-FEC (blue lines), and HD-FEC (red lines).3. CONCLUSIONSIn this paper we discussed the use of information-theoretic metrics (achievable information rates) in the designof optical networks. It was shown that achievable information rates are a powerful design tool for networks thatuse forward error correction and multilevel modulation. The main focus of this paper was on uniform trafficand idealised forward error correction. Future work includes analysis of dynamic traffic scenarios and practicalcodes. We believe the methodology discussed in this paper can be used in such cases.REFERENCES[1] G. Ungerboeck, “Channel coding with multilevel/phase signals,” IEEE Trans. Inf. Theory, vol. 28, no. 1, pp. 55–67, Jan. 1982.[2] L. Szczecinski and A. Alvarado, Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design. 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Designing adaptive coded modulation for optical networks via achievable information rates

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