9,798 research outputs found
An Upper Bound to Zero-Delay Rate Distortion via Kalman Filtering for Vector Gaussian Sources
We deal with zero-delay source coding of a vector Gaussian autoregressive
(AR) source subject to an average mean squared error (MSE) fidelity criterion.
Toward this end, we consider the nonanticipative rate distortion function
(NRDF) which is a lower bound to the causal and zero-delay rate distortion
function (RDF). We use the realization scheme with feedback proposed in [1] to
model the corresponding optimal "test-channel" of the NRDF, when considering
vector Gaussian AR(1) sources subject to an average MSE distortion. We give
conditions on the vector Gaussian AR(1) source to ensure asymptotic
stationarity of the realization scheme (bounded performance). Then, we encode
the vector innovations due to Kalman filtering via lattice quantization with
subtractive dither and memoryless entropy coding. This coding scheme provides a
tight upper bound to the zero-delay Gaussian RDF. We extend this result to
vector Gaussian AR sources of any finite order. Further, we show that for
infinite dimensional vector Gaussian AR sources of any finite order, the NRDF
coincides with the zero-delay RDF. Our theoretical framework is corroborated
with a simulation example.Comment: 7 pages, 6 figures, accepted for publication in IEEE Information
Theory Workshop (ITW
Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
We deal with zero-delay source coding of a vector-valued Gauss-Markov source
subject to a mean-squared error (MSE) fidelity criterion characterized by the
operational zero-delay vector-valued Gaussian rate distortion function (RDF).
We address this problem by considering the nonanticipative RDF (NRDF) which is
a lower bound to the causal optimal performance theoretically attainable (OPTA)
function and operational zero-delay RDF. We recall the realization that
corresponds to the optimal "test-channel" of the Gaussian NRDF, when
considering a vector Gauss-Markov source subject to a MSE distortion in the
finite time horizon. Then, we introduce sufficient conditions to show existence
of solution for this problem in the infinite time horizon. For the asymptotic
regime, we use the asymptotic characterization of the Gaussian NRDF to provide
a new equivalent realization scheme with feedback which is characterized by a
resource allocation (reverse-waterfilling) problem across the dimension of the
vector source. We leverage the new realization to derive a predictive coding
scheme via lattice quantization with subtractive dither and joint memoryless
entropy coding. This coding scheme offers an upper bound to the operational
zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then
for "r" active dimensions of the vector Gauss-Markov source the gap between the
obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1
bits/vector. We further show that it is possible when we use vector
quantization, and assume infinite dimensional Gauss-Markov sources to make the
previous gap to be negligible, i.e., Gaussian NRDF approximates the operational
zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian
sources of any finite memory under mild conditions. Our theoretical framework
is demonstrated with illustrative numerical experiments.Comment: 32 pages, 9 figures, published in IEEE Journal of Selected Topics in
Signal Processin
An Achievable Rate Region for the Broadcast Channel with Feedback
A single-letter achievable rate region is proposed for the two-receiver
discrete memoryless broadcast channel with generalized feedback. The coding
strategy involves block-Markov superposition coding, using Marton's coding
scheme for the broadcast channel without feedback as the starting point. If the
message rates in the Marton scheme are too high to be decoded at the end of a
block, each receiver is left with a list of messages compatible with its
output. Resolution information is sent in the following block to enable each
receiver to resolve its list. The key observation is that the resolution
information of the first receiver is correlated with that of the second. This
correlated information is efficiently transmitted via joint source-channel
coding, using ideas similar to the Han-Costa coding scheme. Using the result,
we obtain an achievable rate region for the stochastically degraded AWGN
broadcast channel with noisy feedback from only one receiver. It is shown that
this region is strictly larger than the no-feedback capacity region.Comment: To appear in IEEE Transactions on Information Theory. Contains
example of AWGN Broadcast Channel with noisy feedbac
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