35,008 research outputs found
Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms
It is well known that Shannon's rate-distortion function (RDF) in the colored
quadratic Gaussian (QG) case can be parametrized via a single Lagrangian
variable (the "water level" in the reverse water filling solution). In this
work, we show that the symmetric colored QG multiple-description (MD) RDF in
the case of two descriptions can be parametrized in the spectral domain via two
Lagrangian variables, which control the trade-off between the side distortion,
the central distortion, and the coding rate. This spectral-domain analysis is
complemented by a time-domain scheme-design approach: we show that the
symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma
modulation and differential pulse-code modulation. Specifically, two source
prediction loops, one for each description, are embedded within a common noise
shaping loop, whose parameters are explicitly found from the spectral-domain
characterization.Comment: Accepted for publications in the IEEE Transactions on Information
Theory. Title have been shortened, abstract clarified, and paper
significantly restructure
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
Online Reinforcement Learning for Dynamic Multimedia Systems
In our previous work, we proposed a systematic cross-layer framework for
dynamic multimedia systems, which allows each layer to make autonomous and
foresighted decisions that maximize the system's long-term performance, while
meeting the application's real-time delay constraints. The proposed solution
solved the cross-layer optimization offline, under the assumption that the
multimedia system's probabilistic dynamics were known a priori. In practice,
however, these dynamics are unknown a priori and therefore must be learned
online. In this paper, we address this problem by allowing the multimedia
system layers to learn, through repeated interactions with each other, to
autonomously optimize the system's long-term performance at run-time. We
propose two reinforcement learning algorithms for optimizing the system under
different design constraints: the first algorithm solves the cross-layer
optimization in a centralized manner, and the second solves it in a
decentralized manner. We analyze both algorithms in terms of their required
computation, memory, and inter-layer communication overheads. After noting that
the proposed reinforcement learning algorithms learn too slowly, we introduce a
complementary accelerated learning algorithm that exploits partial knowledge
about the system's dynamics in order to dramatically improve the system's
performance. In our experiments, we demonstrate that decentralized learning can
perform as well as centralized learning, while enabling the layers to act
autonomously. Additionally, we show that existing application-independent
reinforcement learning algorithms, and existing myopic learning algorithms
deployed in multimedia systems, perform significantly worse than our proposed
application-aware and foresighted learning methods.Comment: 35 pages, 11 figures, 10 table
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