37 research outputs found
On linear H∞ equalization of communication channels
As an alternative to existing techniques and algorithms, we investigate the merit of the H∞ approach to the linear equalization of communication channels. We first give the formulation of all causal H∞ equalizers using the results of and then look at the finite delay case. We compare the risk-sensitive H∞ equalizer with the MMSE equalizer with respect to both the average and the worst-case BER performances and illustrate the improvement due to the use of the H∞ equalizer
A Bayesian Perspective for Determinant Minimization Based Robust Structured Matrix Factorizatio
We introduce a Bayesian perspective for the structured matrix factorization
problem. The proposed framework provides a probabilistic interpretation for
existing geometric methods based on determinant minimization. We model input
data vectors as linear transformations of latent vectors drawn from a
distribution uniform over a particular domain reflecting structural
assumptions, such as the probability simplex in Nonnegative Matrix
Factorization and polytopes in Polytopic Matrix Factorization. We represent the
rows of the linear transformation matrix as vectors generated independently
from a normal distribution whose covariance matrix is inverse Wishart
distributed. We show that the corresponding maximum a posteriori estimation
problem boils down to the robust determinant minimization approach for
structured matrix factorization, providing insights about parameter selections
and potential algorithmic extensions
On the convergence of subgradient based blind equalization algorithm
In this article, we analyze the convergence behavior of the SGBA algorithm for the case where the relaxation rule is used for the step size. Our analysis shows that the monotonic convergence curve for the mean square distance to the optimal point is bounded between two geometric-series curves, and the convergence rate is dependent on the eigenvalues of the correlation matrix of channel outputs. We also provide some simulation examples for the verification of our analytical results related to the convergence behavior
H^∞ equalization of communication channels
As an alternative to existing techniques and algorithms, we investigate the merit of the H-infinity approach to the equalization of communication channels. We first look at causal H-infinity equalization problem and then look at the improvement due to finite delay. By introducing the risk sensitive property, we compare the average performance of the central H-infinity equalizer with the MMSE equalizer in equalizing minimum phase channels
On robust signal reconstruction in noisy filter banks
We study the design of synthesis filters in noisy filter bank systems using an H∞ estimation point of view. The H∞ approach is most promising in situations where the statistical properties of the disturbances (arising from quantization, compression, etc.) in each subband of the filter bank is unknown, or is too difficult to model and analyze. For the important special case of unitary analysis polyphase matrices we obtain an explicit expression for the minimum achievable disturbance attenuation. For arbitrary analysis polyphase matrices, standard state-space H∞ techniques can be employed to obtain numerical solutions. When the synthesis filters are restricted to being FIR, as is often the case in practice, the design can be cast as a finite-dimensional semi-definite program. In this case, we can effectively exploit the inherent non-uniqueness of the H∞ solution to optimize for an additional criteria. By optimizing for average performance in addition to the H∞ criteria, we obtain mixed H^2/H∞ optimal FIR synthesis filters. Alternatively, if the additional criteria is concerned with penalizing occasional occurrence of large values of reconstruction errors more than frequent occurrence of small to moderate ones, we obtain risk-sensitive FIR synthesis filters. Numerical examples and comparisons with existing methods are also included
FIR H∞ equalization
We approach FIR equalization problem from an H∞ perspective.
First, we formulate the calculation of the optimal H∞ performance for a given equalization setting as a semidefinite programming (SDP) problem. H∞ criterion provides a set of FIR equalizers with different optimality properties.
Among
these,
we
formulate
the
calculation
of risk sensitive
or
minimum
entropy
FIR
filter
as
the
constrained analytic centring
problem
and
mixed
H2/H"
problem
as
another
SDP. We
provide an
example
to
il-
lustrate the
procedures
we
described
Correlative Information Maximization: A Biologically Plausible Approach to Supervised Deep Neural Networks without Weight Symmetry
The backpropagation algorithm has experienced remarkable success in training large-scale artificial neural networks; however, its biological plausibility has been strongly criticized, and it remains an open question whether the brain employs supervised learning mechanisms akin to it. Here, we propose correlative information maximization between layer activations as an alternative normative approach to describe the signal propagation in biological neural networks in both forward and backward directions. This new framework addresses many concerns about the biological-plausibility of conventional artificial neural networks and the backpropagation algorithm. The coordinate descent-based optimization of the corresponding objective, combined with the mean square error loss function for fitting labeled supervision data, gives rise to a neural network structure that emulates a more biologically realistic network of multi-compartment pyramidal neurons with dendritic processing and lateral inhibitory neurons. Furthermore, our approach provides a natural resolution to the weight symmetry problem between forward and backward signal propagation paths, a significant critique against the plausibility of the conventional backpropagation algorithm. This is achieved by leveraging two alternative, yet equivalent forms of the correlative mutual information objective. These alternatives intrinsically lead to forward and backward prediction networks without weight symmetry issues, providing a compelling solution to this long-standing challenge