Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications - the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.

The visually evoked magnetic response (VEMR) to a pattern onset/offset stimulus

This study characterizes the visually evoked magnetic response (VEMR) to pattern onset/offset stimuli, using a single channel BTi magnetometer. The influence of stimulus parameters and recording protocols on the VEMR is studied with inferences drawn about the nature of cortical processing, its origins and optimal recording strategies. Fundamental characteristics are examined, such as the behaviour of successive averaged and unaveraged responses; the effects of environmental shielding; averaging; inter- and intrasubject variability and equipment specificity. The effects of varying check size, field size, contrast and refractive error on latency, amplitude and topographic distribution are also presented. Latency and amplitude trends are consistent with previous VEP findings and known anatomical properties of the visual system. Topographic results are consistent with the activity of sources organised according to the cruciform model of striate cortex. A striate origin for the VEMR is also suggested by the results to quarter, octant and annulus field stimuli. Similarities in the behaviour and origins of the sources contributing to the CIIm and CIIIm onset peaks are presented for a number of stimulus conditions. This would be consistent with differing processing event in the same, or similar neuronal populations. Focal field stimuli produce less predictable responses than full or half fields, attributable to a reduced signal to noise ratio and an increased sensitivity to variations in cortical morphology. Problems with waveform peak identification are encountered for full field stimuli that can only be resolved by the careful choice of stimulus parameters, comparisons with half field responses or with reference to the topographic distribution of each waveform peak. An anatomical study of occipital lobe morphology revealed large inter- and intrasubject variation in calcarine fissure shape and striate cortex distribution. An appreciation of such variability is important for VEMR interpretation, due to the technique's sensitivity to source depth and orientation, and it is used to explain the experimental results obtained.

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.

Multispectral imaging of the ocular fundus using light emitting diode illumination

We present an imaging system based on light emitting diode (LED) illumination that produces multispectral optical images of the human ocular fundus. It uses a conventional fundus camera equipped with a high power LED light source and a highly sensitive electron-multiplying charge coupled device camera. It is able to take pictures at a series of wavelengths in rapid succession at short exposure times, thereby eliminating the image shift introduced by natural eye movements (saccades). In contrast with snapshot systems the images retain full spatial resolution. The system is not suitable for applications where the full spectral resolution is required as it uses discrete wavebands for illumination. This is not a problem in retinal imaging where the use of selected wavelengths is common. The modular nature of the light source allows new wavelengths to be introduced easily and at low cost. The use of wavelength-specific LEDs as a source is preferable to white light illumination and subsequent filtering of the remitted light as it minimizes the total light exposure of the subject. The system is controlled via a graphical user interface that enables flexible control of intensity, duration, and sequencing of sources in synchrony with the camera. Our initial experiments indicate that the system can acquire multispectral image sequences of the human retina at exposure times of 0.05 s in the range of 500-620 nm with mean signal to noise ratio of 17 dB (min 11, std 4.5), making it suitable for quantitative analysis with application to the diagnosis and screening of eye diseases such as diabetic retinopathy and age-related macular degeneration.

Noise characterization and transmission evaluation of unrepeated Raman amplified DP-16QAM link

Impairments characterization and performance evaluation of Raman amplified unrepeated DP-16QAM transmissions are conducted. Experimental results indicate that small gain in forward direction enhance the system signal-to-noise ratio for longer reach without introducing noticeable penalty.

Experimental comparison of coherent polarization-switched QPSK to polarization-multiplexed QPSK for 10 x 100 km WDM transmission

Polarization-switched quadrature phase-shift keying has been demonstrated experimentally at 40.5Gb/s with a coherent receiver and digital signal processing. Compared to polarization-multiplexed QPSK at the same bit rate, its back-to-back sensitivity at 10-3 bit-error-ratio shows 0.9dB improvement, and it tolerates about 1.6dB higher launch power for 10 × 100km, 50GHz-spaced WDM transmission allowing 1dB penalty in required optical-signal-to-noise ratio relative to back-to-back.

Noise and gain optimisation in bi-directionally pumped dispersion compensating amplifier modules

We perform optimisation of bi-directionally pumped dispersion compensating Raman amplifier modules. Optimal forward and backward pump powers for basic configurations using different commercially available fibers are presented for both single- and multi-channel systems. Optical signal-to-noise ratio improvement of up to 8 dB is achieved as a result of optimisation. © 2003 Published by Elsevier B.V.

Analytical BER performance in differential n-PSK coherent transmission system influenced by equalization enhanced phase noise

Long-haul high speed optical transmission systems are significantly distorted by the interplay between the electronic chromatic dispersion (CD) equalization and the local oscillator (LO) laser phase noise, which leads to an effect of equalization enhanced phase noise (EEPN). The EEPN degrades the performance of optical communication systems severely with the increment of fiber dispersion, LO laser linewidth, symbol rate, and modulation format. In this paper, we present an analytical model for evaluating the performance of bit-error-rate (BER) versus signal-to-noise ratio (SNR) in the n-level phase shift keying (n-PSK) coherent transmission system employing differential carrier phase estimation (CPE), where the influence of EEPN is considered. Theoretical results based on this model have been investigated for the differential quadrature phase shift keying (DQPSK), the differential 8-PSK (D8PSK), and the differential 16-PSK (D16PSK) coherent transmission systems. The influence of EEPN on the BER performance in term of the fiber dispersion, the LO phase noise, the symbol rate, and the modulation format are analyzed in detail. The BER behaviors based on this analytical model achieve a good agreement with previously reported BER floors influenced by EEPN. Further simulations have also been carried out in the differential CPE considering EEPN. The results indicate that this analytical model can give an accurate prediction for the DQPSK system, and a leading-order approximation for the D8PSK and the D16PSK systems.

Interleavers and BCH codes for coherent DQPSK systems with laser phase noise

The relatively high phase noise of coherent optical systems poses unique challenges for forward error correction (FEC). In this letter, we propose a novel semianalytical method for selecting combinations of interleaver lengths and binary Bose-Chaudhuri-Hocquenghem (BCH) codes that meet a target post-FEC bit error rate (BER). Our method requires only short pre-FEC simulations, based on which we design interleavers and codes analytically. It is applicable to pre-FEC BER ∼10-3, and any post-FEC BER. In addition, we show that there is a tradeoff between code overhead and interleaver delay. Finally, for a target of 10-5, numerical simulations show that interleaver-code combinations selected using our method have post-FEC BER around 2× target. The target BER is achieved with 0.1 dB extra signal-to-noise ratio.

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.

The impact of parametric noise amplification on long haul transmission throughput

Advanced signal processing, such as multi-channel digital back propagation and mid span optical phase conjugation, can compensate for inter channel nonlinear effects in point to point links. However, once such are effects are compensated, the interaction between the signal and noise fields becomes dominant. We will show that this interaction has a direct impact on the signal to noise ratio improvement, observing that ideal optical phase conjugation offers 1.5 dB more performance benefit than DSP based compensation.

Concurrent codes:a holographic-type encoding robust against noise and loss

Concurrent coding is an encoding scheme with 'holographic' type properties that are shown here to be robust against a significant amount of noise and signal loss. This single encoding scheme is able to correct for random errors and burst errors simultaneously, but does not rely on cyclic codes. A simple and practical scheme has been tested that displays perfect decoding when the signal to noise ratio is of order -18dB. The same scheme also displays perfect reconstruction when a contiguous block of 40% of the transmission is missing. In addition this scheme is 50% more efficient in terms of transmitted power requirements than equivalent cyclic codes. A simple model is presented that describes the process of decoding and can determine the computational load that would be expected, as well as describing the critical levels of noise and missing data at which false messages begin to be generated.

Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

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.