21,086 research outputs found
Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources
We improve the existing achievable rate regions for causal and for zero-delay
source coding of stationary Gaussian sources under an average mean squared
error (MSE) distortion measure. To begin with, we find a closed-form expression
for the information-theoretic causal rate-distortion function (RDF) under such
distortion measure, denoted by , for first-order Gauss-Markov
processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically
attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that,
for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq
Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze
for arbitrary zero-mean Gaussian stationary sources, we
introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the
reconstruction error is jointly stationary with the source. Based upon
\bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate
loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two
of these bounds are strictly smaller than 0.5 bits/sample at all rates. These
bounds differ from one another in their tightness and ease of evaluation; the
tighter the bound, the more involved its evaluation. We then show that, for any
source spectral density and any positive distortion D\leq \sigma_{x}^{2},
\bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set
of causal pre-, post-, and feedback filters. We show that finding such filters
constitutes a convex optimization problem. In order to solve the latter, we
propose an iterative optimization procedure that yields the optimal filters and
is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a
connection to feedback quantization we design a causal and a zero-delay coding
scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor
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On designing H∞ filters with circular pole and error variance constraints
Copyright [2003] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we deal with the problem of designing a H∞ filter for discrete-time systems subject to error variance and circular pole constraints. Specifically, we aim to design a filter such that the H∞ norm of the filtering error-transfer function is not less than a given upper bound, while the poles of the filtering matrix are assigned within a prespecified circular region, and the steady-state error variance for each state is not more than the individual prespecified value. The filter design problem is formulated as an auxiliary matrix assignment problem. Both the existence condition and the explicit expression of the desired filters are then derived by using an algebraic matrix inequality approach. The proposed design algorithm is illustrated by a numerical example
Adaptive and Iterative Multi-Branch MMSE Decision Feedback Detection Algorithms for MIMO Systems
In this work, decision feedback (DF) detection algorithms based on multiple
processing branches for multi-input multi-output (MIMO) spatial multiplexing
systems are proposed. The proposed detector employs multiple cancellation
branches with receive filters that are obtained from a common matrix inverse
and achieves a performance close to the maximum likelihood detector (MLD).
Constrained minimum mean-squared error (MMSE) receive filters designed with
constraints on the shape and magnitude of the feedback filters for the
multi-branch MMSE DF (MB-MMSE-DF) receivers are presented. An adaptive
implementation of the proposed MB-MMSE-DF detector is developed along with a
recursive least squares-type algorithm for estimating the parameters of the
receive filters when the channel is time-varying. A soft-output version of the
MB-MMSE-DF detector is also proposed as a component of an iterative detection
and decoding receiver structure. A computational complexity analysis shows that
the MB-MMSE-DF detector does not require a significant additional complexity
over the conventional MMSE-DF detector, whereas a diversity analysis discusses
the diversity order achieved by the MB-MMSE-DF detector. Simulation results
show that the MB-MMSE-DF detector achieves a performance superior to existing
suboptimal detectors and close to the MLD, while requiring significantly lower
complexity.Comment: 10 figures, 3 tables; IEEE Transactions on Wireless Communications,
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