The bit error probability (BER) and the generalized cutoff rate (GCR) of optically amplified, direct-detection on-off keying (OOK) signaling are addressed utilizing the classical theory of Fredholm integral equations. The approach accounts for the impact of optical bandlimiting and upper bounds on the BER are found via Chernoff techniques, which address the resultant intersymbol interference (ISI) incurred by the linear pulse distortion. Simple rigorous upper bounds on the BER are derived in terms of basic system parameters relaxing the need for solving Fredholm related equations. Random coding is used to obtain the GCR of this channel. The theory is demonstrated for the Lorentzian and finite-duration bandpass optical filters and the optical bandwidth which optimally balances the ISI versus the amplified spontaneous emission noise is found.>

Low to moderate complexity coding schemes are suggested and examined for binary DPSK modulation. The model of the communication channel consists of both a Brownian motion phase noise and an additive white Gaussian noise. Decoding utilizes a mismatched soft-decision metric, which comprises the prefiltering of the phase noise impaired signals followed by differential demodulation. The resulting equivalent, binary-input, output-symmetric, discrete-time, coding channel is stationary and memoryless. It accounts as well for an underlying time-diversity, thus providing an effective simple, means of boosting the capabilities of less powerful codes to cope with the existing phase noise levels. An analytical upper bound on the coded error probability is derived, which strictly addresses the Brownian motion phase model. It features a convenient decoupling of the code structure from the coding channel. The latter is completely specified via a single, scalar, generic parameter which relies on the univariate moments admitted by certain exponential functionals of the Brownian motion sample path, the exact statistics of which is intractable. The theory is illustrated while studying the performance of low constraint length, rate 1/n, binary convolutional codes, which are optimally combined with time-diversity. The advantages obtained by less trivial forms of code concatenation are examined. The approach treated is to use a two level concatenation scheme for which the binary inner code dimension matches the alphabet size of an outer non-binary code.>

The distribution law of the Brownian motion exponential functional: /spl epsiv/=|f/sub [0,1]/exp[j/spl radic/(2/spl beta/W/sub t/]dt|/sup 2/), where {W/sub t/,t/spl isin//spl Rscr//sup +/} is a standard Brownian motion, modeling the laser's phase noise, plays a key role in many of the proposed heterodyne lightwave systems. The exact analytic derivation of these statistics appears to be, however, a formidable mathematical task. We present a closed form formula for the kth power moment E/spl epsiv//sup k/ induced by the unknown distribution law. The results are useful in assessing the performance of noisy phase lightwave systems.>

Differential phase shift keying (DPSK) in the presence of both additive white Gaussian noise and a phase impairment, modeled by a Brownian motion is considered. A time-diversity scheme is used for mitigating the effects of phase noise. This scheme renders a repetition coding approach where the transmitter sends multiple replicas of each data bit. An upper bound on the bit error probability, relying on a bivariate moment-generating function admitted by certain real functionals of the phase sample-path, is derived. The approach taken yields a trackable analysis, which rigorously adheres the phase noise effects. The impact of an incomplete statistical characterization on the tightness of the resultant bound is addressed. The theory, which is applicable to assess the design and performance of general heterodyned lightwave systems using (delay) differential demodulation (as DPSK and CP-FSK, or continuous phase frequency-shift keying), is exemplified and explicit results for the considered time-diversity DPSK scheme are provided. The optimum design of the diversity level is discussed and it is concluded that power efficient transmission is feasible even at bit rates comparable with the signal linewidth.>

In the above-named work (see ibid., vol.39, no.11, p.1635-50, Nov.1991) Appendixes A-C contained computer transcription related errors during the publishing process which rendered them useless to the reader. The corrected versions, are presented.>

The performance of noncoherent detection of orthogonal phase-noise impaired signals in the presence of additive white Gaussian noise is considered. The authors present a novel class of upper and lower bounds on the error probability of a binary hypothesis test, comprising quadratic forms of the additive noise and of the filtered noisy-phase signal plus noise. Filtering the noisy-phase signal gives rise to bounded nonlinear functionals of the Brownian motion sample-path, the exact statistics of which are unknown. The classical theory of Chebyshev systems is utilized to solve the limiting values of the required stochastic expectations, based on the availability of the corresponding generalized moments. The resulting multidimensional moment bounds constitute the tightest possible error bounds for the given set of generalized moments, and require only modest computational efforts. The theory is applicable to assess the design and performance of optical heterodyne systems and is most suitable for coded systems employing hard-decisions, for which the obtained bounds are remarkably tight.>

A rigorous method to find the upper bound of the error probability of noncoherent quadratically detected signals in the presence of both additive white Gaussian noise and Brownian carrier phase noise is presented. An analytical upper bound on the bit error probability is derived, relying on a bivariate moment-generating function of two bounded exponential functionals of the Brownian phase path. These functionals, whose exact statistics are unknown, yield the two basic impairments arising due to phase noise: in-band signal suppression and intersymbol crosstalk . The classical theory of Chebyshev systems is applied to obtain the limiting values of the involved generating function, utilizing a multidimensional moment characterization of the involved functionals. The impact of the incomplete-statistical characterization used on the resultant upper-bound tightness is addressed. Assessing the design and performance of lightwave heterodyned systems using this method is discussed. The method enables the analysis of interchannel crosstalk effects in frequency-division multiplexing systems.>