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Abstract Terabit Optical Ethernet (TOE) will be affectednot only by limited bandwidth of information-infrastructure, but

also by its energy consumption. In order to solve both problems

simultaneously, in this invited paper, we describe several energy-

efficient (EE) hybrid-coded-modulation (CM) schemes enabling

TOE: EE-hybrid-multidimensional-CM, EE-generalized-OFDM,

and EE-spatial-domain-based-CM.

I. INTRODUCTION

The exponential internet traffic growth projections require

considerable increase of transmission data rates at every level

of the underlying information infrastructure, from core

networks to access networks. Higher volumes of traffic also

increase the energy consumption of transmission and

switching equipment needed to route this traffic. Recent

studies indicate that the energy consumed by the Internetequipment is roughly 8% of the total energy consumed in the

US with predictions that it can grow up to 50%, with current

trend, by the end of this decade [1],[2]. Therefore, the Internet

is becoming constrained not only by capacity, but also by its

energy consumption.

In order to solve high-bandwidth demands and energy-

efficiency problems simultaneously, in this invited paper, we

describe several energy-efficient (EE) hybrid coded-

modulation (CM) schemes enabling Terabit Optical Ethernet:

energy-efficient multidimensional coded-modulation [3], EE

generalized-OFDM [4], EE 4D-multiband-coded-OFDM [5],

and EE spatial-domain-based-coded-modulation [6]. Due to

space limitations, the first two schemes are described here, the

other schemes will be presented at the conference. Commonproperties of these schemes are: the employment of energy-

efficient coded-modulations, the employment of multiple

degrees of freedom for the conveyance of the information on

single-carrier optical signal and rate-adaptive coding based on

quasi-cyclic LDPC codes. These EE schemes are called hybrid

as they employ all available degrees of freedom for the

transmission over optical fiber including amplitude, phase,

polarization and orbital angular momentum (OAM). Namely,

from Shannons theory we know that the channel capacity is a

linear function in number of dimensions, and by increasing

the number of dimensionsbasis functions originating from

different degrees of freedom that are mutually orthogonal in

naturewe can dramatically improve the overall channel

capacity. On the other hand, the energy-efficiency problemcan be solved by properly designing the multi-dimensional

signal constellations such that the trans-information is

maximized, while taking the energy constraint into account.

These hybrid coded-modulation schemes are very flexible, as

they can be used for various applications ranging from short-

haul to long-haul, and can be used in SMF, MMF and free-

space optical links.

This paper was supported in part by NSF under grant CCF-0952711, and in

part by NEC Labs.

II. ENERGY-EFFICIENT SIGNAL CONSTELLATION DESIGN

The basic EE optical communication problem can be

formulated as follows. The symbols to be transmitted over

optical channel of interest are chosen from the followings set

X={x1, x2,,xM}. The symbols from this set have energies

E1,,EM and occur with a priori probabilities p1,,pM[pi=Pr(xi)]. The symbols from the set Xsatisfy the probability

constraint, ipi=1, and energy constraint, ipiEiE. In the

presence of various channel impairments; such as fiber

nonlinearities, PMD, and PDL; and ASE noise; the

Lagranagian method can be used in maximizing the trans-

information (also known as mutual information) I(X,Y),

defined as I(X,Y)=H(X)-H(X|Y), where H(X) is the entropy of

the channel input X and H(X|Y) is the conditional entropy of

channel inputXgiven the channel output Y. To determine the

optimum signal constellation, the energy-efficient Arimoto-

Blahut algorithm (EE-ABA) can be used as we described in

[3]. As an illustration, in Fig. 1 we report the information

capacities for different normalized energy cost functions for

number of amplitude levels per dimension L. In Fig. 1, we

provide the results corresponding to coherent detection. It is

clear from the Figure, that when the normalized energy cost

function is lower than one, we are facing certain information

capacity degradation.

8 12 16 20 24 281

2

3

4

Capacity,

C[(bits/chaneluse)/dimension]

Signal-to-noise ratio per symbol, SNRs[dB]

L=4:

no rmalized energy cost:

1 0.75

0.5

L=8:

no rmalized energy cost:

1 0.750.5

L=16:

normalized energy cost:

1 0.75

0.5

Fig. 1. Information capacities per dimension for different normalized

energy cost values and different number of amplitude levels per

dimensionLin coherent detection case.

III. EEHYBRID MULTIDIMENSIONAL CMSCHEMES

The coordinates of the EE signal constellation from D-

dimensional mapper, implemented as a single look-up-table

(LUT), are used as the inputs to theD-dimensional modulator.

This modulator generates the signal constellation points by [3]

,

=1

= C ,D

i D i d d

d

s f (1)

Coding and Modulation Techniques Enabling

Multi-Tb/s Optical EthernetIvan B. Djordjevic

University of Arizona, Department of Electrical and Computer Engineering, Tucson, AZ 85721, USA; E-mail: ivan@email.arizona.edu

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MW1 (Invited)1:30 PM 2:00 PM

978-1-4244-8939-8/11/$26.00 2011 IEEE

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where i,d denotes the dth coordinate (d=1,,D) of the ith

signal-constellation point, the set {1,,D} represents the

set of D=2MN orthogonal bases functions, where factor two

comes from two orthogonal polarization states, Ndenotes the

number of orthogonal OAM eigenstates and M basis

functions are defined as

m(nT)=exp[j2(m-1)nT/Ts] (m=1,,M) (2)

where Ts is the symbol duration, and T is the sampling

interval, related to symbol duration by T=Ts/U, with U being

the oversampling factor. (In Eq. (1), CD denotes the

normalization factor.) The EE signal constellation coordinates

are split into N groups of 2M-coordinates per each OAM

mode. The 2M-coordinates of each group are used as input of

2M-dimesnional modulator, composed of two polarization-

multiplexed M-dimensional modulators. (Alternatively, one

2M-dimensional modulator can be used.) The M signal-

constellation point coordinates after up-sampling are passed

through corresponding discrete-time (DT) pulse-shaping

filters of impulse responses hm(n)=m(nT), whose outputs are

combined together into a single complex data stream. After

separation of real and imaginary parts and digital-to-analog

conversion (DAC), the corresponding Re- and Im-parts areused as inputs to I/Q modulator.

On receiver side, we first perform OAM mode-

demultiplexing, with OAM-demux block outputs representing

the projections alongNOAM states. The nth OAM projection,

which is a 2M-dimensional signal, is used as input to the

polarization-beam splitter (PBS). The x-polarization (y-

polarization) signal, being itself an M-dimensional signal, is

used as input to the balanced coherent detector. After coherent

detection we recover Re- and Im-parts, which are after analog-

to-digital conversion (ADC) combined into a single complex

data stream. The same complex data stream is applied to the

inputs of Mmatched filters of impulse responses hm(n)= m(-

nT). The corresponding outputs after re-sampling represent

projections along basis functions m. At this point all 2MN-coordinates of EE D-dimensional signal constellations are

estimated, and corresponding coordinate estimates

(representing the projections along D-basis functions) are

forwarded to the D-dimensional a posteriori probability

(APP) demapper, which calculates symbol log-likelihood

ratios (LLRs). From symbol LLRs we calculate the bit

likelihoods needed for LDPC decoding. For more details

about this scheme an interested reader is referred to [3].

The spectral efficiency of this hybrid D-dimensional

scheme, whereD=2MN, is-dim. constellation

2 2

PDM-QAM

2 QAM 2 QAM

log log

2log 2log

D D

E

E

S L D L

S M M (3)

times better than that of polarization-division-multiplexed(PDM) QAM scheme. In (3), with MQAM we denoted the

QAM signal constellation size. Therefore, for the same

number of amplitude levels per dimension (MQAM=L2), the

spectral efficiency of the proposed scheme is (D/4)-times

better than that of PDM-QAM. The aggregate data rate (per

single wavelength) is determined by

2

2 s

ch. bits ch. sym. info. bitslog ( ) ,

ch. sym. s ch. bits

MNL R r (4)

where r is the code rate, which is assumed to be equal for

LDPC codes at each level, and Rs is the symbol rate. As an

illustrative example, by setting L=4, M=8, Rs=50 GS/s, and

r=0.8, the aggregate data rate of 1.28Tb/s per single OAM

mode is obtained. By varying the number of OAM modes up

to ten, the total aggregate data rate can be increased up to

fantastic 12.8 Tb/s per single wavelength. The numerical

results will be presented at the conference.

IV. EEGENERALIZEDOFDM(EE-GOFDM)

The key idea behind the coded generalized OFDM (GOFDM)

[4] scheme is to increase the number dimensions over which

the signal constellation is defined in order to realize optical

transmission systems that are not only spectrally more

efficient but also more immune to channel impairments. We

call this scheme as a generalization of OFDM since we

consider theNorthogonal subcarriers of OFDM as a set of N

basis functions. The N-dimensional signal constellation is

obtained by using the concept outlined in Sec. II. We depicted

in Figs. 2(top) and (bottom) the transmitter and receiver

configurations for EE-GOFDM scheme. As it can be seen inFig.2, when operated at the symbol rate of Rs the GOFDM

scheme provides 2Rslog2(LN) bits per second aggregate bit

rate, where the coefficient of two comes from the polarization-

multiplexing. As an illustrative example, when the symbol rate

is set to Rs=25 GS/s (50 GS/s) and N=10, L=4 are used, the

aggregate bit rate reaches 1 Tb/s (2 Tb/s).

IFFTCyclic extension

insertion and

P/S conversion

LPF

LPF

DAC

DAC

Source

channels

(x-pol.)

1

b

Interleaverbxn

b

N-dim.

symbolsLDPC encoderr=k/ n

LDPC encoderr=k/ n

to fiber

Ix

LDPC-coded EE-GOFDM

EEN-dim.

mapper

4D modulator

Qx

IyQy

1

b

.

.

.

LDPC

decoder 1

.

.

.

N-dim. APP

Demapper

and

Bit LLRs

Calculator

Extrinsic LLRs

LDPC

decoder b

From

SMF

Local

LaserPBS

PBSLPF

LPF

ADC

ADCFFT

Balanced coherent

detector (x pol.)

Cyclic extension

removal and

and S/P conversion

Balanced coherent

detector (y pol.) Fig. 2 EE-GOFDM architecture: (top) Tx and (bottom) Rx configurations.

The common denominator of EE multidimensional CM

schemes described above is the employment of rate-adaptive

quasi-cyclic (QC) LDPC codes in FEC, which can adapt FEC

strength based on channel conditions. The idea is to deliver

data with target BER regardless of the destination.

REFERENCES

[1] B. G. Bathula, M. Alresheedi, and J. M. H Elmirghani, Energy efficient

architectures for optical networks, in Proc. IEEE London

Communications Symposium, London, Sept. 2009.

[2] N. Vasic, and D. Kostic, Energy-aware traffic engineering EPFL

Technical Report, 2008.

[3] I. B. Djordjevic, Energy-efficient spatial-domain-based hybrid

multidimensional coded-modulations enabling multi-Tb/s opticaltransport, Opt. Express, accepted for publication.

[4] I. B. Djordjevic, M. Arabaci, L. Xu, T. Wang, Generalized OFDM

(GOFDM) for ultra-high-speed optical transmission, Opt. Express, vol.

19, no. 7, pp. 6969-6979, 2011.

[5] I. Djordjevic, H. G. Batshon, L. Xu, T. Wang, Four-dimensional optical

multiband-OFDM for beyond 1.4 Tb/s serial optical transmission, Opt.

Express, vol. 19, no. 2, pp. 876-882, 2011.

[6] I. B. Djordjevic, M. Arabaci, L. Xu, T. Wang, Spatial-domain-based

multidimensional modulation for multi-Tb/s serial optical transmission,

Opt. Express, vol. 19, no. 7, pp. 6845-6857, 2011.

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