IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 45, NO. 8, AUGUST 1997 965

Optical Duobinary Modulationwith Alleviated Phase Constraints

D. Penninckx

Abstract—Spectral compression is a necessary function for ap-plications in optical communication such as noise reduction, useof bandwidth-limited devices, etc. Ideal duobinary modulation,which allows the reduction of the spectrum bandwidth, requiresa � (rad) phase shift between the “�1” and the “ +1” logicallevels. We show that with a reasonable finite extinction ratio of10 dB, a phase shift as low as0:18� can be used, with a resultingspectrum compression ratio of nearly 2.

Index Terms—Codes, digital communication, optical fiber com-munication, optical fiber dispersion.

I. INTRODUCTION

I N order to overcome the penalty induced by the chromaticdispersion of standard dispersive fibers, a new method has

been proposed: spectrum compression by appropriate coding[1]–[5]. Duobinary coding [6] was thus suggested, whichallows a twofold reduction of the bandwidth of an NRZsignal, and is simple to implement. However, it has beenshown recently that spectrum compression is not the relevantparameter to assess chromatic dispersion tolerance [7], [8].Another way to take advantage of duobinary coding is toconvert the detected electrical binary signal into a duobinarysignal in order to reduce the bandwidth and hence the noiselevel [9]. This can also be performed by using an opticalduobinary signal with three intensity levels. Furthermore, sincefiber gratings, used to compensate for the chromatic dispersion,are bandwidth limited, it is interesting to compress the spectralbandwidth of the signal. Recently, 700 km have been achievedat 10 Gbit/s over standard dispersive fiber [10]. Spectralcompression was achieved by the use of duobinary coding.However, this requires a phase shift between the “ ” andthe “ ” logical levels of the code. In this paper, we showanalytically and numerically that this phase shift requirementcan be reduced to about , and even to betweenconsecutive bits with a compression factor of nearly 2. Thismethod is called pseudoduobinary coding.

II. OPTICAL DUOBINARY MODULATION

Two schemes have been used for optical duobinary trans-mission. The first one [1], [2] considers an intensity duobinary

. However, it also requires two thresholds in thereceiver. Furthermore, this is not the ideal duobinary sincethe field amplitude levels, which are the relevant levels tocalculate the optical spectrum, are and . The

Paper approved by J. J. O’Reilly, the Editor for Optical Communicationsof the IEEE Communications Society. Manuscript received July 15, 1996;revised December 15, 1996.

The author is with Alcatel Alsthom Recherche, 91460 Marcoussis, France.Publisher Item Identifier S 0090-6778(97)05742-5.

second one [3]–[5] consists of using the phase of the opticalwave leading to the use of the amplitude levels:

. The -phase shift can be performed with a LiNbOMach–Zehnder modulator in push–pull mode, but becauseof the phase-amplitude coupling, it is almost impossible toachieve such a phase shift with an electroabsorption modulator.In addition, the influence of the finite extinction ratio has notbeen yet analyzed. In this paper, we also show that, even bytaking into account the finite extinction ratio, in both schemes,the optical spectrum is nearly contracted by a factor of 2.

III. GENERAL CASE

Consider three complex amplitude levels:, , andwhere represents the logical “0,” and and are the logical“ ” and “ ” levels, respectively. They follow the same ruleas a duobinary signal, i.e., a binary signal is converted into,

, and such as a “0” is converted into “” and each group of“ ” is translated into a group of identical length of either “”or “ ” If the number of “0” between two groups of “” is odd,the state remains “” or “ .” If this number is even, the statechanges from “ ” to “ ” or from “ ” to “ ” For instance,the sequence “ ” is trans-lated into “ .”

In the first scheme described in Section II, ,and , and in the second scheme,

, and , where is the phase ofthe logical “0” and is the extinction ratio between “1” and“0” levels.

For compound logical levels, the optical spectral densitycan be written as

(1)

where and are the continuous and discrete parts of thespectral density, respectively, is the bit time, is theFourier transform of the pulse envelope, is the mean valueof the logical levels, and is the difference between thecovariance of two bits of the sequence separated byand . Following the method described in [1] for complexamplitudes, one finds

0090–6778/97$10.00 1997 IEEE

966 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 45, NO. 8, AUGUST 1997

Fig. 1. Numerically calculated spectra of a 1024-bit-long sequence with pseudo-duobinary coding in four different cases (the Dirac peaks were removed forclarity by substracting the mean values).m = 0: ideal binary coding(A = B = 1; Z = 0); m = 1=3: A = ei0:10� ; B = e�i0:10� , andZ = 1=

p10;

m = 2=3: A = ei0:18� ; B = e�i0:18� , andZ = 1=p10; m = 1: A = ei0:397� ; B = e�i0:397� , andZ = 1=

p10.

(2)

and, when where denotes complexconjugation.

Thus, for a rectangular pulse shape,

and

where

(3)

The case corresponds to the binary coding ,whereas , leading to an optimum spectrum compression,corresponds among others to the ideal duobinary coding

.Setting , and can also be

written

(4)

Since , oneobtains

(5)

The case corresponds to , i.e.,

(6)

The numerically calculated spectra in four cases correspondingto , and are shown in Fig. 1. From thisfigure, we can perhaps consider that is enough toachieve a spectral compression by nearly a factor of 2.

The first scheme described in Section II with ,and leads to . When taking into accountthe finite extinction ratio, e.g., with , and

, it leads to . The second scheme with, and yields . In all

of these cases, is well above 2/3, resulting in a sufficientcompression of the spectrum.

IV. PRACTICAL CASE

The practical case is shown in Fig. 2, where the geomet-rical representation of , and is sketched. This casecorresponds to and having the same intensity and beingpositioned symmetrically with respect to.Thus, , where is the extinc-tion ratio and (3) leads to

(7)

PENNINCKX: OPTICAL DUOBINARY MODULATION WITH ALLEVIATED PHASE CONSTRAINTS 967

(a) (b)

Fig. 2. (a) Practical case, positions ofA; B, andZ whenA=Z = (B=Z)�

=pEei�=2. (b) Practical case whenm = 1.

Fig. 3. Contour plot of the modulation index in the(E; �) plane. The blackarea corresponds tom < 2=3. The dotted line is� = 2 arccos (1=

pE),

leading tom = 1. The dashed lines correspond tom = 0:95. Note that whenE = 10 dB, the phase difference can be decreased to0:36� (64�), leadingto a phase difference between to neighboring bits as low as0:18� (32�).

In this case, the condition (6) for which is equal to 1becomes (see Fig. 2)

(8)

Thus, ideal duobinary coding is not the only way to achieveoptimal spectral compression. For instance, when ,then for optimum compression of the opticalspectrum. Furthermore, in duobinary coding, there is no directtransition or : there is always at least oneinbetween. Thus, the phase difference between two neighboringbits is as low as for a 10-dB extinction ratio.

Fig. 3 shows the contour plot of in the plane. Forfor . Therefore, the phase

difference between two neighboring bits can be decreasedto . Such a phase variation can be obtained with thechirp of an electroabsoption modulator with negligible residualintensity modulation.

V. CONCLUSION

In summary, we have calculated the spectrum of a pseu-doduobinary signal considering three different complex levels

( , and ). In the general case, the condition for optimalspectral compression is . In the practicalcase, where both nonzero levels have the same intensity andare symmetrical with respect to the zero level, a relationshipbetween the phase difference between the two nonzero levelsand the extinction ratio is derived. Ideal duobinary coding isa particular case for which the extinction ratio is infinite andthe phase shift is equal to. It was shown that, in order toreduce the optical spectrum bandwidth of the sequence nearlyby a factor of 2, it is not necessary to increase the extinctionratio as much as possible and to set the phase shift to. Forinstance, with a 10 dB extinction ratio, the phase differencebetween neighboring bits can be reduced to ,equivalent to an 82% reduction. This technique may be usedin every application where a twofold spectral compression ofan NRZ signal with a carrier frequency is needed either in theoptical or in the electrical domain.

ACKNOWLEDGMENT

The author would like to thank A. Penninckx and V.Morenas for their help in the calculations.

REFERENCES

[1] X. Gu and L. C. Blank, “10 Gbit/s unrepeatered three-level opticaltransmission over 100 km standard fiber,”Elecron. Lett., vol. 29, no.25, pp. 2209–2211, Dec. 1993.

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D. Penninckx was born in 1970 in Paris, France.He graduated from theEcole Normale Superieurede Lyon (Normale Sup Lyon, 1989–1993) and re-ceived the Engineering Degree in electrical and elec-tronic sciences fromEcole Superieure d’Electricite(Supelec, 1991–1993) in Gif-sur-Yvette (France).He returned from military service in 1994, and iscurrently working toward the Ph.D. degree. His dis-sertation is on novel modulation formats in opticalcommunications.

During 1992–1993, he spent nearly one year intraining at Alcatel Alsthom Recherche, Marcoussis, France.