Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Wireless Communications

Information Theory and Reliable Communication

Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.

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Bit-Interleaved Coded Modulation

This paper considers the transmission of confidential data over wireless channels. Based on an information-theoretic formulation of the problem, in which two legitimates partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through a second independent quasi-static fading channel, the important role of fading is characterized in terms of average secure communication rates and outage probability. Based on the insights from this analysis, a practical secure communication protocol is developed, which uses a four-step procedure to ensure wireless information-theoretic security: (i) common randomness via opportunistic transmission, (ii) message reconciliation, (iii) common key generation via privacy amplification, and (iv) message protection with a secret key. A reconciliation procedure based on multilevel coding and optimized low-density parity-check (LDPC) codes is introduced, which allows to achieve communication rates close to the fundamental security limits in several relevant instances. Finally, a set of metrics for assessing average secure key generation rates is established, and it is shown that the protocol is effective in secure key renewal-even in the presence of imperfect channel state information.

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Wireless Information-Theoretic Security

Various modifications to conventional information coding schemes that result in an improvement in one or more performance measures for a given coding scheme. Some examples are directed to improved decoding techniques for linear block codes, such as low-density parity-check (LDPC) codes. In one example, modifications to a conventional belief-propagation (BP) decoding algorithm for LDPC codes significantly improve the performance of the decoding algorithm so as to more closely approximate that of the theoretically optimal maximum-likelihood (ML) decoding scheme. BP decoder performance generally is improved for lower code block lengths, and significant error floor reduction or elimination may be achieved for higher code block lengths. In one aspect, significantly improved performance of a modified BP algorithm is achieved while at the same time essentially maintaining the benefits of relative computational simplicity and execution speed of a conventional BP algorithm as compared to an ML decoding scheme. In another aspect, modifications for improving the performance of conventional BP decoders are universally applicable to “off the shelf” LDPC encoder/decoder pairs. Furthermore, the concepts underlying the various methods and apparatus disclosed herein may be more generally applied to various decoding schemes involving iterative decoding algorithms and message-passing on graphs, as well as coding schemes other than LDPC codes to similarly improve their performance. Exemplary applications for improved coding schemes include wireless (mobile) networks, satellite communication systems, optical communication systems, and data recording and storage systems (e.g., CDs, DVDs, hard drives, etc.).

Methods and apparatus for improving performance of information coding schemes

In this paper, we present an algebraic methodology for implementing low-complexity, Chase-type, decoding of Reed-Solomon (RS) codes of length n . In such, a set of 2 ? test-vectors that are equivalent on all except ? ? n coordinate positions is first produced. The similarity of the test-vectors is utilized to reduce the complexity of interpolation, the process of constructing a set of polynomials that obey constraints imposed by each test-vector. By first considering the equivalent indices, a polynomial common to all test-vectors is constructed. The required set of polynomials is then produced by interpolating the final ? dissimilar indices utilizing a binary-tree structure. In the second decoding step (factorization) a candidate message is extracted from each interpolation polynomial such that one may be chosen as the decoded message. Although an expression for the direct evaluation of each candidate message is provided, carrying out this computation for each polynomial is extremely complex. Thus, a novel, reduced-complexity, methodology is also given. Although suboptimal, simulation results affirm that the loss in performance incurred by this procedure is decreasing with increasing code length n, and negligible for long (n > 100) codes. Significant coding gains are shown to be achievable over traditional hard-in hard-out decoding procedures (e.g., Berlekamp-Massey) at an equivalent (and, in some cases, lower) computational complexity. Furthermore, these gains are shown to be similar to the recently proposed soft-in-hard-out algebraic techniques (e.g., Sudan, Ko?tter-Vardy) that bear significantly more complex implementations than the proposed algorithm.

Low-Complexity Soft-Decoding Algorithms for Reed–Solomon Codes—Part I: An Algebraic Soft-In Hard-Out Chase Decoder

A method of determining branch metric values in a detector. The method includes receiving a plurality of time variant signal samples, the signal samples having one of signal-dependent noise, correlated noise, and both signal dependent and correlated noise associated therewith. The method also includes selecting a branch metric function at a certain time index and applying the selected function to the signal samples to determine the metric values.

Soft and hard sequence detection in ISI memory channels

In high density magnetic recording, noise samples corresponding to adjacent signal samples are heavily correlated as a result of front-end equalizers, media noise, and signal nonlinearities combined with nonlinear filters to cancel them. This correlation significantly deteriorates the performance of detectors at high densities. In this paper, we propose a novel sequence detector that is correlation sensitive and adaptive to the nonstationary signal sample statistics. We derive the correlation-sensitive maximum likelihood detector. It can be used with any Viterbi-like receiver (e.g., partial response maximum likelihood, fixed delay tree search, multilevel decision feedback equalization) that relies on a tree/trellis structure. Our detector adjusts the metric computation to the noise correlation statistics. Because these statistics are nonstationary, we develop an adaptive algorithm that tracks the data correlation matrices. Simulation results are presented that show the applicability of the new correlation-sensitive adaptive sequence detector.

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Correlation-sensitive adaptive sequence detection

We present a statistical model for the path loss of ultra-wideband (UWB) channels in indoor environments. In contrast to our previously reported measurements, the data reported here are for a bandwidth of 6GHz rather than 1.25GHz; they encompass commercial buildings in addition to single-family homes (20 of each); and local spatial averaging is included. As before, the center frequency is 5.0GHz. Separate models are given for commercial and residential environments and, within each category, for line-of-sight (LOS) and non-line-of-sight (NLS) paths. All four models have the same mathematical structure, differing only in their numerical parameters. The two new models (LOS and NLS) for residences closely match those derived from the previous measurements, thus affirming the stability of our path loss modeling. We find, also, that the path loss statistics for the two categories of buildings are quite similar.

Aleksandar Kavcic

Papers

Methods and apparatus for improving performance of information coding schemes

Low-Complexity Soft-Decoding Algorithms for Reed–Solomon Codes—Part I: An Algebraic Soft-In Hard-Out Chase Decoder

Soft and hard sequence detection in ISI memory channels

Correlation-sensitive adaptive sequence detection

An empirical indoor path loss model for ultra-wideband channels