Dimensioning BCH codes for coherent DQPSK systems with laser phase noise and cycle slips

Forward error correction (FEC) plays a vital role in coherent optical systems employing multi-level modulation. However, much of coding theory assumes that additive white Gaussian noise (AWGN) is dominant, whereas coherent optical systems have significant phase noise (PN) in addition to AWGN. This changes the error statistics and impacts FEC performance. In this paper, we propose a novel semianalytical method for dimensioning binary Bose-Chaudhuri-Hocquenghem (BCH) codes for systems with PN. Our method involves extracting statistics from pre-FEC bit error rate (BER) simulations. We use these statistics to parameterize a bivariate binomial model that describes the distribution of bit errors. In this way, we relate pre-FEC statistics to post-FEC BER and BCH codes. Our method is applicable to pre-FEC BER around 10-3 and any post-FEC BER. Using numerical simulations, we evaluate the accuracy of our approach for a target post-FEC BER of 10-5. Codes dimensioned with our bivariate binomial model meet the target within 0.2-dB signal-to-noise ratio.

A comparison of denoising methods for X-ray fluoroscopic images

Fluoroscopic images exhibit severe signal-dependent quantum noise, due to the reduced X-ray dose involved in image formation, that is generally modelled as Poisson-distributed. However, image gray-level transformations, commonly applied by fluoroscopic device to enhance contrast, modify the noise statistics and the relationship between image noise variance and expected pixel intensity. Image denoising is essential to improve quality of fluoroscopic images and their clinical information content. Simple average filters are commonly employed in real-time processing, but they tend to blur edges and details. An extensive comparison of advanced denoising algorithms specifically designed for both signal-dependent noise (AAS, BM3Dc, HHM, TLS) and independent additive noise (AV, BM3D, K-SVD) was presented. Simulated test images degraded by various levels of Poisson quantum noise and real clinical fluoroscopic images were considered. Typical gray-level transformations (e.g. white compression) were also applied in order to evaluate their effect on the denoising algorithms. Performances of the algorithms were evaluated in terms of peak-signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), mean square error (MSE), structural similarity index (SSIM) and computational time. On average, the filters designed for signal-dependent noise provided better image restorations than those assuming additive white Gaussian noise (AWGN). Collaborative denoising strategy was found to be the most effective in denoising of both simulated and real data, also in the presence of image gray-level transformations. White compression, by inherently reducing the greater noise variance of brighter pixels, appeared to support denoising algorithms in performing more effectively. © 2012 Elsevier Ltd. All rights reserved.

Low-complexity BCH codes with optimized interleavers for DQPSK systems with laser phase noise

The presence of high phase noise in addition to additive white Gaussian noise in coherent optical systems affects the performance of forward error correction (FEC) schemes. In this paper, we propose a simple scheme for such systems, using block interleavers and binary Bose–Chaudhuri–Hocquenghem (BCH) codes. The block interleavers are specifically optimized for differential quadrature phase shift keying modulation. We propose a method for selecting BCH codes that, together with the interleavers, achieve a target post-FEC bit error rate (BER). This combination of interleavers and BCH codes has very low implementation complexity. In addition, our approach is straightforward, requiring only short pre-FEC simulations to parameterize a model, based on which we select codes analytically. We aim to correct a pre-FEC BER of around (Formula presented.). We evaluate the accuracy of our approach using numerical simulations. For a target post-FEC BER of (Formula presented.), codes selected using our method result in BERs around 3(Formula presented.) target and achieve the target with around 0.2 dB extra signal-to-noise ratio.

Typical performance of low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.

Structured codebooks for SCS watermarking

Digital watermarking aims at embedding information in digital data. The watermark is usually required to be imperceptible, unremovable and to have a high information content. Unfortunately, these three requirements are contradicting. For example, having a more robust watermark makes it either more perceptible or/and less informative. For Gaussian data and additive white Gaussian noise, an optimal but also impractical scheme has already be devised. Since then, many practical schemes have tried to approach the theoretical limits. This paper investigate improvements to current state-of-the-art embedding schemes.

Pulse compression applied to the detection of F.S.K. and P.S.K. signals

The matched filter detector is well known as the optimum detector for use in communication, as well as in radar systems for signals corrupted by Additive White Gaussian Noise (A.W.G.N.). Non-coherent F.S.K. and differentially coherent P.S.K. (D.P.S.K.) detection schemes, which employ a new approach in realizing the matched filter processor, are investigated. The new approach utilizes pulse compression techniques, well known in radar systems, to facilitate the implementation of the matched filter in the form of the Pulse Compressor Matched Filter (P.C.M.F.). Both detection schemes feature a mixer- P.C.M.F. Compound as their predetector processor. The Compound is utilized to convert F.S.K. modulation into pulse position modulation, and P.S.K. modulation into pulse polarity modulation. The mechanisms of both detection schemes are studied through examining the properties of the Autocorrelation function (A.C.F.) at the output of the P.C.M.F.. The effects produced by time delay, and carrier interference on the output A.C.F. are determined. Work related to the F.S.K. detection scheme is mostly confined to verifying its validity, whereas the D.P.S.K. detection scheme has not been reported before. Consequently, an experimental system was constructed, which utilized combined hardware and software, and operated under the supervision of a microprocessor system. The experimental system was used to develop error-rate models for both detection schemes under investigation. Performances of both F. S. K. and D.P. S. K. detection schemes were established in the presence of A. W. G. N. , practical imperfections, time delay, and carrier interference. The results highlight the candidacy of both detection schemes for use in the field of digital data communication and, in particular, the D.P.S.K. detection scheme, which performed very close to optimum in a background of A.W.G.N.

Data transmission by frequency-hopped multilevel frequency shift keying

Spread spectrum systems make use of radio frequency bandwidths which far exceed the minimum bandwidth necessary to transmit the basic message information.These systems are designed to provide satisfactory communication of the message information under difficult transmission conditions. Frequency-hopped multilevel frequency shift keying (FH-MFSK) is one of the many techniques used in spread spectrum systems. It is a combination of frequency hopping and time hopping. In this system many users share a common frequency band using code division multiplexing. Each user is assigned an address and the message is modulated into the address. The receiver, knowing the address, decodes the received signal and extracts the message. This technique is suggested for digital mobile telephony. This thesis is concerned with an investigation of the possibility of utilising FH-MFSK for data transmission corrupted by additive white gaussian noise (A.W.G.N.). Work related to FH-MFSK has so far been mostly confined to its validity, and its performance in the presence of A.W.G.N. has not been reported before. An experimental system was therefore constructed which utilised combined hardware and software and operated under the supervision of a microprocessor system. The experimental system was used to develop an error-rate model for the system under investigation. The performance of FH-MFSK for data transmission was established in the presence of A.W.G.N. and with deleted and delayed sample effects. Its capability for multiuser applications was determined theoretically. The results show that FH-MFSK is a suitable technique for data transmission in the presence of A.W.G.N.

Sparsely spread CDMA - A statistical mechanics-based analysis

Sparse code division multiple access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains only a relatively small number of nonzero elements, is presented and analysed using methods of statistical physics. The analysis provides results on the performance of maximum likelihood decoding for sparse spreading codes in the large system limit. We present results for both cases of regular and irregular spreading matrices for the binary additive white Gaussian noise channel (BIAWGN) with a comparison to the canonical (dense) random spreading code. © 2007 IOP Publishing Ltd.

Typical performance of regular low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Relationship between the free energy in statistical-mechanics approach and the mutual information used in the information-theory literature is established within a general framework; Gallager and MacKay-Neal codes are studied as specific examples of LDPC codes. It is shown that basic properties of these codes known for particular channels, including their potential to saturate Shannon's bound, hold for general symmetric channels. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel models.

Design of nonlinear regenerative transmission systems with high capacity

We present the design of nonlinear regenerative communication channels that have capacity above the classical Shannon capacity of the linear additive white Gaussian noise channel. The upper bound for regeneration efficiency is found and the asymptotic behavior of the capacity in the saturation regime is derived. © 2013 IEEE.

Detection of signals corrupted by the combination of Gaussian and Non-Gaussian noise

The detection of signals in the presence of noise is one of the most basic and important problems encountered by communication engineers. Although the literature abounds with analyses of communications in Gaussian noise, relatively little work has appeared dealing with communications in non-Gaussian noise. In this thesis several digital communication systems disturbed by non-Gaussian noise are analysed. The thesis is divided into two main parts. In the first part, a filtered-Poisson impulse noise model is utilized to calulate error probability characteristics of a linear receiver operating in additive impulsive noise. Firstly the effect that non-Gaussian interference has on the performance of a receiver that has been optimized for Gaussian noise is determined. The factors affecting the choice of modulation scheme so as to minimize the deterimental effects of non-Gaussian noise are then discussed. In the second part, a new theoretical model of impulsive noise that fits well with the observed statistics of noise in radio channels below 100 MHz has been developed. This empirical noise model is applied to the detection of known signals in the presence of noise to determine the optimal receiver structure. The performance of such a detector has been assessed and is found to depend on the signal shape, the time-bandwidth product, as well as the signal-to-noise ratio. The optimal signal to minimize the probability of error of; the detector is determined. Attention is then turned to the problem of threshold detection. Detector structure, large sample performance and robustness against errors in the detector parameters are examined. Finally, estimators of such parameters as. the occurrence of an impulse and the parameters in an empirical noise model are developed for the case of an adaptive system with slowly varying conditions.

Regeneration limit of classical Shannon capacity

Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit -the upper bound of regeneration efficiency -is derived. © 2014 Macmillan Publishers Limited. All rights reserved.

The effect of Gaussian noise on the threshold, dynamic range, and loudness of analogue cochlear implant stimuli

The deliberate addition of Gaussian noise to cochlear implant signals has previously been proposed to enhance the time coding of signals by the cochlear nerve. Potentially, the addition of an inaudible level of noise could also have secondary benefits: it could lower the threshold to the information-bearing signal, and by desynchronization of nerve discharges, it could increase the level at which the information-bearing signal becomes uncomfortable. Both these effects would lead to an increased dynamic range, which might be expected to enhance speech comprehension and make the choice of cochlear implant compression parameters less critical (as with a wider dynamic range, small changes in the parameters would have less effect on loudness). The hypothesized secondary effects were investigated with eight users of the Clarion cochlear implant; the stimulation was analogue and monopolar. For presentations in noise, noise at 95% of the threshold level was applied simultaneously and independently to all the electrodes. The noise was found in two-alternative forced-choice (2AFC) experiments to decrease the threshold to sinusoidal stimuli (100 Hz, 1 kHz, 5 kHz) by about 2.0 dB and increase the dynamic range by 0.7 dB. Furthermore, in 2AFC loudness balance experiments, noise was found to decrease the loudness of moderate to intense stimuli. This suggests that loudness is partially coded by the degree of phase-locking of cochlear nerve fibers. The overall gain in dynamic range was modest, and more complex noise strategies, for example, using inhibition between the noise sources, may be required to get a clinically useful benefit. © 2006 Association for Research in Otolaryngology.

Regression with input-dependent noise: A Bayesian treatment

In most treatments of the regression problem it is assumed that the distribution of target data can be described by a deterministic function of the inputs, together with additive Gaussian noise having constant variance. The use of maximum likelihood to train such models then corresponds to the minimization of a sum-of-squares error function. In many applications a more realistic model would allow the noise variance itself to depend on the input variables. However, the use of maximum likelihood to train such models would give highly biased results. In this paper we show how a Bayesian treatment can allow for an input-dependent variance while overcoming the bias of maximum likelihood.

Statistics of noise-driven coupled nonlinear oscillators:applications to systems with Kerr nonlinearity

We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength. © 2005 Elsevier B.V. All rights reserved.