Non-circular or improper Gaussian signaling has proven beneficial in several interference-limited wireless networks. However, all implementable coding schemes are based on finite discrete constellations rather than Gaussian signals. In this paper, we propose a new family of improper constellations generated by widely linear processing of a square M-QAM (quadrature amplitude modulation) signal. This family of discrete constellations is parameterized by κ, the circularity coefficient and a phase φ. For uncoded communication systems, this phase should be optimized as φ * (κ) to maximize the minimum Euclidean distance between points of the improper constellation, therefore minimizing the bit error rate (BER). For the more relevant case of coded communications, where the coded symbols are constrained to be in this family of improper constellations using φ * (κ), it is shown theoretically and further corroborated by simulations that, except for a shaping loss of 1.53 dB encountered at a high signal-to-noise ratio (snr), there is no rate loss with respect to the improper Gaussian capacity. In this sense, the proposed family of constellations can be viewed as the improper counterpart of the standard proper M-QAM constellations widely used in coded communication systems.
Quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. Moreover, quantum channel models that are efficiently implementable and manageable on classical computers are required in order to design and simulate such error correction schemes. In this paper, we present a survey of decoherence models, reviewing the manner in which these models can be approximated into quantum Pauli channel models, which can be efficiently implemented on classical computers. We also explain how certain families of quantum error correction codes can be entirely simulated in the classical domain, without the explicit need of a quantum computer. A quantum error correction code for the approximated channel is also a correctable code for the original channel, and its performance can be obtained by Monte Carlo simulations on a classical computer. INDEX TERMS Decoherence, quantum channels, quantum error correction, Gottesman-Knill theorem.
A decision feedback equalizer (DFE) containing a feedback filter with both poles and zeroes i s proposed for highspeed digital communications over the subscriber loop. The feedback filter is composed of two sections: a relatively short finite impulse response (FIR) filter that cancels the initial part of the channel impulse response, which may contain rapid variations due to bridge taps; and a pole-zero, or IIR, filter that cancels the smoothly decaying tail of the impulse response. Modifications of an existing adaptive IIR algorithm, based on the Steiglitz-McBride identification scheme, are proposed to adapt the feedback filter. These new algorithms have comparable complexity to gradient-based adaptive IIR algorithms when the number of poles is small, but converge significantly faster. A measured subscriber loop impulse response is used to compare the performance of the adaptive pole-zero DFE, assuming a two-pole feedback filter, with a conventional DFE having the same number of coefficients. Results show that the pole-zero DFE offers a significant improvement in mean squared error (i.e., 4 dB at a signal-to-noise ratio of 25 dB) relative to the conventional DFE. Furthermore, the speed of convergence of the adaptive pole-zero DFE is comparable with that of the conventional DFE using the standard LMS adaptive algorithm.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.