Multicarrier signals are known to suffer from a high peak-to-average power ratio, caused by the addition of a large number of independently modulated subcarriers in parallel at the transmitter. When subjected to a peak-limiting channel, such as a nonlinear power amplifier, these signals may undergo significant spectral distortion, leading to both in-band and out-of-band interference, and an associated degradation in system performance. This paper characterizes the distortion caused by the clipping of multicarrier signals in a peak-limiting (nonlinear) channel. Rather than modeling the effects of distortion as additive noise, as is widespread in the literature, we identify clipping as a rare event and focus on evaluating system performance based on the conditional probability of bit error given the occurrence of such an event. Our analysis is based on the asymptotic properties of the large excursions of a stationary Gaussian process, and offers important insights into both the true nature of clipping distortion, as well as the consequent design of schemes to alleviate this problem.

Digital subscriber line (DSL) technology for high-speed data transmission over the local-loop telephone twisted pairs was advanced in the labs of several research institutions during the late 1980’s and early 1990’s. Researchers began to develop and experiment with new transmission ideas and to realize high-speed modems in prototype form. As technology matured and standards evolved, these modems came to be known collectively as “xDSL” modems. The ISDN basic-rate interface, which was developed during the early 1980’s and operated at a “mere” 160 kb/s, today is often cited as being the archetype of this technology.

The encoding and decoding schemes presented are aimed at enabling the transfer of data through a channel in which two types of interference are added to the transmitted signal and the sum is quantized. One of these interferences is known (or can be estimated), whereas the second is an additive white Gaussian noise (AWGN). Since the input of the quantizer is not accessible, the known interference can not be removed from the received signal. We show that the error rate for an uncoded transmission through this channel is unacceptably large, even for low noise levels and linear quantization. It is also shown that the problem becomes even more severe when a nonlinear quantization is present. Therefore, coding is essential and a huge coding gain is achievable in this application. An upper-bound on the error rate, contributed by the component codes of a multilevel code, has been developed for multistage decoding. Results of computer simulations of a practical case with optimal and suboptimal decoding algorithms, both developed in this paper, are presented.

The effect of the companding process on QAM signals has been under investigation for the past several years. The compander, included in the PCM telephone network to improve voice performance, has an unusual affect on digital QAM data signals which are transmitted over the same channel. The quantization noise, generated by the companding process which is multiplicative (and asymmetric), degrades the detectability performance of the outermost points of the QAM constellation more than that of the inner points. The combined effect of the companding noise and the inherent white Gaussian noise of the system, leads to a re-examination of signal constellation design. The authors investigate the detectability performance of a number of candidates for signal constellations including, a typical rectangular QAM constellation, the same constellation with the addition of a smear-desmear operation, and two new improved QAM constellation designs with two-dimensional warping.>

The authors investigate the efficacy of using two different cyclic redundancy check (CRC) codes in tandem to increase error-burst detecting capability. For a set of pairs of CRCs which are used in standards, it is found that the guaranteed detectable burst length is less than the sum of the individual guaranteed detectable burst lengths, but not much less. Thus strengthened CRC codes can readily be obtained using existing devices.>

When a QAM (quadrature amplitude modulation) data signal is transmitted over a channel that includes PCM codecs, it has frequently been observed and shown that the resulting noise around the final received constellation points grows with the distance of the point from the origin. The authors extend the analysis of this effect, and further show that the noise distribution about each point is elliptical, with greater variance in the radial direction. Formulas giving the signal-dependent noise components as a function of the channel characteristics of the analog transmit and receive access legs are derived. Experimental results confirm the analysis.>

The problems of clocking data across the interface between synchronous data networks are considered. Maximum time interval error is introduced as a specification which includes both phase and frequency errors.

It is shown in the classification problem, when independent samples are taken from uniform distributions, that for small sample sizes the probability of misclassification when using the nearest-neighbor rule is "close" to its asymptotic value. It is also shown that when using this rule the probability of classification in many cases is close to its Bayes optimum even for small sample sizes. Moreover, if one is restricted to a small sample size from one population, it is shown that it is not necessary to "make up" this deficiency by taking a large sample from the other population; best results may be obtained when both sample sizes are small.

An upper bound is derived for the probability of error of a digital communication system subject to intersymbol interference and Gaussian noise. The bound is applicable to multilevel as well as binary signals and to all types of intersymbol interference. The bound agrees with the exponential portion of a normal distribution in which the larger intersymbol interference components subtract from the signal amplitude, and the smaller components add to the noise power. The results are applied to the case of random binary signaling with sinx/xpulses. It is shown that such signals are not so sensitive to timing error as is commonly believed, nor does the total signal amplitude become very large with significant probability. However, the error probability does grow very rapidly as the system bandwidth is reduced below the Nyquist band.