Abstract

Electronic signal processing is becoming very attractive to overcome various impairments that affect optical communications, and electronic dispersion compensation (EDC) represents a typical application in the currently designed systems. However, the inherent limits in performance achievable by electronically processing the signal at the output of a nonlinear photodetector have not received the attention they deserve. In this paper, we investigate the information-theoretic limits of electronic signal processing in transmission systems employing direct photodetection and two possible modulation formats: 1) on–off keying (OOK) with nonreturn-to-zero pulses; and 2) optical duobinary modulation (ODBM). The analysis is based on the computation of the information rate, i.e., the maximum achievable data transfer rate, and accounts for the modulation format as well as relevant parameters of the transmission scheme. In particular, we investigate the impact of sampling rate, uncompensated chromatic dispersion (CD), and quantization resolution of the electrical signal at the output of a direct photodetector. For OOK systems, the obtained results show that the optical signal-to-noise ratio penalty entailed by EDC can be limited to about 2 dB at most values of CD of interest in current applications. Moreover, ODBM systems at high values of CD can almost perform as OOK systems at zero CD. For all the considered modulation formats, the obtained results show that the received electrical signal can be sampled at a rate of two samples per bit interval and quantized with a precision of 3 bits per sample to practically achieve the ultimate performance limits.

© 2007 IEEE

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  9. D. E. Crivelli, H. S. Carrer, M. R. Hueda, "On the performance of reduced-state Viterbi receivers in IM/DD optical transmission systems ," Proc. ECOC (2004) pp. 634-635.
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2006 (7)

G. Bosco, P. Poggiolini, "Long-distance effectiveness of MLSE IMDD receivers," IEEE Photon. Technol. Lett. 18, 1037-1039 (2006).

T. Foggi, E. Forestieri, G. Colavolpe, G. Prati, "Maximum likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD," J. Lightw. Technol. 24, 3073-3087 (2006).

D. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, W. Zen, "Simulation-based computation of information rates for channel with memory," IEEE Trans. Inf. Theory 52, 3498-3508 (2006).

J. Tang, "A comparison study of the Shannon channel capacity of various nonlinear optical fibers ," J. Lightw. Technol. 24, 2070-2075 (2006).

M. Franceschini, G. Ferrari, R. Raheli, G. Bongiorni, "Fundamental limits of electronic dispersion compensation in optical communications with direct photodetection," Electron. Lett. 42, 874-875 (2006).

P. J. Winzer, R. Essiambre, "Advanced optical modulation formats," Proc. IEEE 94, 952-985 (2006).

M. Jager, T. Rankl, J. Speidel, H. Bulow, F. Buchali, "Performance of turbo equalizers for optical PMD channels," J. Lightw. Technol. 24, 1226-1236 (2006).

2005 (3)

I. B. Djordjevic, B. Vasic, M. Ivkovic, I. Gabitov, "Achievable information rates for high-speed long-haul optical transmission," J. Lightw. Technol. 23, 3755-3763 (2005).

G. Ferrari, G. Colavolpe, R. Raheli, "A unified framework for finite-memory detection," IEEE J. Sel. Areas Commun. 23, 1697-1706 (2005).

O. E. Agazzi, M. R. Hueda, H. S. Carrer, D. E. Crivelli, "Maximum-likelihood sequence estimation in dispersive optical channels," J. Lightw. Technol. 23, 749-763 (2005).

2004 (1)

V. Curri, R. Gaudino, A. Napoli, P. Poggiolini, "Electronic equalization for advanced modulation formats in dispersion-limited systems ," IEEE Photon. Technol. Lett. 16, 2556-2558 (2004).

2002 (1)

E. E. Narimanov, P. Mitra, "The channel capacity of a fiber optics communication system: Perturbation theory," J. Lightw. Technol. 20, 530-537 (2002).

2001 (1)

J. Tang, "The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission ," J. Lightw. Technol. 19, 1104-1109 (2001).

2000 (1)

E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering," J. Lightw. Technol. 18, 1493-1503 (2000).

1997 (1)

K. Yonenaga, S. Kuwano, "Dispersion-tolerant optical transmission system using duobinary transmitter and binary receiver ," J. Lightw. Technol. 15, 1530-1537 (1997).

1996 (1)

C. Berrou, A. Glavieux, "Near optimum error correcting coding and decoding: Turbo-codes," IEEE Trans. Commun. 44, 1261-1271 (1996).

1995 (1)

C. Douillard, M. Jezequel, C. Berrou, A. Picart, P. Didier, A. Glavieux, "Iterative correction of intersymbol interference: Turbo-equalization," Eur. Trans. Telecommun. 6, 507-511 (1995).

1991 (1)

S. Shamai, "On the capacity of a direct-detection photon channel with intertransition-constrained binary input ," IEEE Trans. Inf. Theory 37, 1540-1550 (1991).

1990 (1)

J. H. Winters, R. D. Gitlin, "Signal processing techniques in long-haul fiber-optic systems," IEEE Trans. Commun. 38, 1439-1453 (1990).

1974 (1)

L. R. Bahl, J. Cocke, F. Jelinek, J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory IT-20, 284-287 (1974).

Electron. Lett. (1)

M. Franceschini, G. Ferrari, R. Raheli, G. Bongiorni, "Fundamental limits of electronic dispersion compensation in optical communications with direct photodetection," Electron. Lett. 42, 874-875 (2006).

Eur. Trans. Telecommun. (1)

C. Douillard, M. Jezequel, C. Berrou, A. Picart, P. Didier, A. Glavieux, "Iterative correction of intersymbol interference: Turbo-equalization," Eur. Trans. Telecommun. 6, 507-511 (1995).

IEEE J. Sel. Areas Commun. (1)

G. Ferrari, G. Colavolpe, R. Raheli, "A unified framework for finite-memory detection," IEEE J. Sel. Areas Commun. 23, 1697-1706 (2005).

IEEE Photon. Technol. Lett. (2)

V. Curri, R. Gaudino, A. Napoli, P. Poggiolini, "Electronic equalization for advanced modulation formats in dispersion-limited systems ," IEEE Photon. Technol. Lett. 16, 2556-2558 (2004).

G. Bosco, P. Poggiolini, "Long-distance effectiveness of MLSE IMDD receivers," IEEE Photon. Technol. Lett. 18, 1037-1039 (2006).

IEEE Trans. Commun. (2)

J. H. Winters, R. D. Gitlin, "Signal processing techniques in long-haul fiber-optic systems," IEEE Trans. Commun. 38, 1439-1453 (1990).

C. Berrou, A. Glavieux, "Near optimum error correcting coding and decoding: Turbo-codes," IEEE Trans. Commun. 44, 1261-1271 (1996).

IEEE Trans. Inf. Theory (3)

S. Shamai, "On the capacity of a direct-detection photon channel with intertransition-constrained binary input ," IEEE Trans. Inf. Theory 37, 1540-1550 (1991).

L. R. Bahl, J. Cocke, F. Jelinek, J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory IT-20, 284-287 (1974).

D. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, W. Zen, "Simulation-based computation of information rates for channel with memory," IEEE Trans. Inf. Theory 52, 3498-3508 (2006).

J. Lightw. Technol. (9)

K. Yonenaga, S. Kuwano, "Dispersion-tolerant optical transmission system using duobinary transmitter and binary receiver ," J. Lightw. Technol. 15, 1530-1537 (1997).

J. Tang, "The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission ," J. Lightw. Technol. 19, 1104-1109 (2001).

E. E. Narimanov, P. Mitra, "The channel capacity of a fiber optics communication system: Perturbation theory," J. Lightw. Technol. 20, 530-537 (2002).

J. Tang, "A comparison study of the Shannon channel capacity of various nonlinear optical fibers ," J. Lightw. Technol. 24, 2070-2075 (2006).

T. Foggi, E. Forestieri, G. Colavolpe, G. Prati, "Maximum likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD," J. Lightw. Technol. 24, 3073-3087 (2006).

O. E. Agazzi, M. R. Hueda, H. S. Carrer, D. E. Crivelli, "Maximum-likelihood sequence estimation in dispersive optical channels," J. Lightw. Technol. 23, 749-763 (2005).

M. Jager, T. Rankl, J. Speidel, H. Bulow, F. Buchali, "Performance of turbo equalizers for optical PMD channels," J. Lightw. Technol. 24, 1226-1236 (2006).

I. B. Djordjevic, B. Vasic, M. Ivkovic, I. Gabitov, "Achievable information rates for high-speed long-haul optical transmission," J. Lightw. Technol. 23, 3755-3763 (2005).

E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering," J. Lightw. Technol. 18, 1493-1503 (2000).

Proc. IEEE (1)

P. J. Winzer, R. Essiambre, "Advanced optical modulation formats," Proc. IEEE 94, 952-985 (2006).

Other (16)

J. G. Proakis, Digital Communications (McGraw-Hill, 2001).

J. Li, "On the achievable information rate of asymmetric optical fiber channels with amplifier spontaneous emission noise," Proc. IEEE MILCOM (2003) pp. 124-129.

R. Ramaswami, K. Sivarajan, Optical Networks (Morgan Kaufman, 2001).

G. Agrawal, Fiber-Optic Communications Systems (Wiley, 2002).

E. W. Weistein, "Levenberg–Marquardt method," From MathWorld—A Wolfram Web Resource http://mathworld.wolfram.com/Levenberg-MarquardtMethod.html.

M. R. Hueda, D. E. Crivelli, H. S. Carrer,, "Performance of MLSE-based receivers in lightwave systems with nonlinear dispersion and amplified spontaneous emission noise," Proc. IEEE GLOBECOM (2004) pp. 299-303.

S. M. Ross, Stochastic Processes (Wiley, 1983).

H. S. Carrer, D. E. Crivelli, M. R. Hueda, "Maximum likelihood sequence estimation receivers for DWDM lightwave systems," Proc. IEEE GLOBECOM (2004) pp. 1005-1010.

H. S. Carrer, M. R. Hueda, D. E. Crivelli, "MLSE-based receivers on DWDM lightwave systems," Proc. 9th ICCS (2004) pp. 573-578.

D. E. Crivelli, H. S. Carrer, M. R. Hueda, "On the performance of reduced-state Viterbi receivers in IM/DD optical transmission systems ," Proc. ECOC (2004) pp. 634-635.

H. Bülow, "Electronic equalization of transmission impairments," Proc. OFC Conf. (2002) pp. 24-25.

C. Xia, W. Rosenkranz, "Performance enhancement for duobinary modulation through nonlinear electrical equalization ," Proc. ECOC (2005) pp. 255-256.

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley, 1991).

D. Arnold, H.-A. Loeliger, "On the information rate of binary-input channels with memory," Proc. IEEE ICC (2001) pp. 2692-2695.

V. Sharma, S. K. Singh, "Entropy and channel capacity in the regenerative setup with applications to Markov channels ," Proc. IEEE ISIT (2001) pp. 283.

H. D. Pfister, J. B. Soriaga, P. H. Siegel, "On the achievable information rates of finite state ISI channels," Proc. GLOBECOM (2001) pp. 2992-2996.

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