42,139 research outputs found
Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems
An algorithm for scalar quantizer design on discrete-alphabet sources is proposed. The proposed algorithm can be used to design fixed-rate and entropy-constrained conventional scalar quantizers, multiresolution scalar quantizers, multiple description scalar quantizers, and Wyner–Ziv scalar quantizers. The algorithm guarantees globally optimal solutions for conventional fixed-rate scalar quantizers and entropy-constrained scalar quantizers. For the other coding scenarios, the algorithm yields the best code among all codes that meet a given convexity constraint. In all cases, the algorithm run-time is polynomial in the size of the source alphabet. The algorithm derivation arises from a demonstration of the connection between scalar quantization, histogram segmentation, and the shortest path problem in a certain directed acyclic graph
Second-Order Coding Rates for Conditional Rate-Distortion
This paper characterizes the second-order coding rates for lossy source
coding with side information available at both the encoder and the decoder. We
first provide non-asymptotic bounds for this problem and then specialize the
non-asymptotic bounds for three different scenarios: discrete memoryless
sources, Gaussian sources, and Markov sources. We obtain the second-order
coding rates for these settings. It is interesting to observe that the
second-order coding rate for Gaussian source coding with Gaussian side
information available at both the encoder and the decoder is the same as that
for Gaussian source coding without side information. Furthermore, regardless of
the variance of the side information, the dispersion is nats squared per
source symbol.Comment: 20 pages, 2 figures, second-order coding rates, finite blocklength,
network information theor
Network vector quantization
We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples
Joint Source-Channel Coding over a Fading Multiple Access Channel with Partial Channel State Information
In this paper we address the problem of transmission of correlated sources
over a fast fading multiple access channel (MAC) with partial channel state
information available at both the encoders and the decoder. We provide
sufficient conditions for transmission with given distortions. Next these
conditions are specialized to a Gaussian MAC (GMAC). We provide the optimal
power allocation strategy and compare the strategy with various levels of
channel state information.
Keywords: Fading MAC, Power allocation, Partial channel state information,
Correlated sources.Comment: 7 Pages, 3 figures. To Appear in IEEE GLOBECOM, 200
Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
We investigate an encoding scheme for lossy compression of a binary symmetric
source based on simple spatially coupled Low-Density Generator-Matrix codes.
The degree of the check nodes is regular and the one of code-bits is Poisson
distributed with an average depending on the compression rate. The performance
of a low complexity Belief Propagation Guided Decimation algorithm is
excellent. The algorithmic rate-distortion curve approaches the optimal curve
of the ensemble as the width of the coupling window grows. Moreover, as the
check degree grows both curves approach the ultimate Shannon rate-distortion
limit. The Belief Propagation Guided Decimation encoder is based on the
posterior measure of a binary symmetric test-channel. This measure can be
interpreted as a random Gibbs measure at a "temperature" directly related to
the "noise level of the test-channel". We investigate the links between the
algorithmic performance of the Belief Propagation Guided Decimation encoder and
the phase diagram of this Gibbs measure. The phase diagram is investigated
thanks to the cavity method of spin glass theory which predicts a number of
phase transition thresholds. In particular the dynamical and condensation
"phase transition temperatures" (equivalently test-channel noise thresholds)
are computed. We observe that: (i) the dynamical temperature of the spatially
coupled construction saturates towards the condensation temperature; (ii) for
large degrees the condensation temperature approaches the temperature (i.e.
noise level) related to the information theoretic Shannon test-channel noise
parameter of rate-distortion theory. This provides heuristic insight into the
excellent performance of the Belief Propagation Guided Decimation algorithm.
The paper contains an introduction to the cavity method
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